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Absolute value equations example 1 | Linear equations | Algebra I | Khan Academy

Video vocabulary

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

stuff

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US / stʌf /

UK / stʌf /

A1
  • noun
  • Generic description for things, materials, objects
  • verb
  • To push material inside something, with force

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

logic

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US / ˈlɒdʒɪk /

UK / ˈlɑ:dʒɪk /

A2
  • noun
  • Proper, valid sensible reasoning
  • Scientific study of reasoning

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

depend

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US / dɪˈpend /

UK / dɪˈpend /

B1
  • verb
  • Be controlled or determined by (someone/something)

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

situation

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US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

remember

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US / rɪ'membə(r) /

UK / rɪˈmɛmbɚ /

A1
  • verb
  • To give someone a gift, e.g. birthday, wedding
  • To hold a thought in your mind to not forget it
  • To bring a previous image or idea to your mind

away

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US / ə'weɪ /

UK / əˈwe /

A1
  • adjecitve
  • Not present
  • adverb
  • Disappear completely
  • Doing something with a lot of energy
  • Not here; far from here; in a different direction
  • To a different area, location

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

whenever

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US / wenˈevə(r) /

UK / hwɛnˈɛvɚ /

A1
  • adverb
  • At any or every time that

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

absolute

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US / ˈæbsəlu:t /

UK / ˈæbsəˌlut /

A2
  • adjecitve
  • Complete; total; pure; not limited in any way
  • noun
  • Something that is complete, total, pure, certain

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

verify

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US / 'verɪfaɪ /

UK / ˈvɛrəˌfaɪ /

B2
  • verb
  • To prove that something is right, accurate or true

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

big

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US / bɪɡ /

UK / bɪɡ /

A1
  • adjecitve
  • Popular
  • Serious
  • Large

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

solution

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US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

inside

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US / ˌɪn'saɪd /

UK / ɪnˈsaɪd, ˈɪnˌsaɪd /

A2
  • adjecitve
  • Being in something
  • Being in a building
  • adverb
  • Into a house; indoors
  • noun
  • Inner part or surface of something

satisfy

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US / ˈsætɪsfaɪ /

UK / ˈsætɪsˌfaɪ /

A2
  • verb
  • To make someone happy because they got their wish
  • To do what is required in order to finish

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

exactly

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US / ɪgˈzæktli /

UK / ɪɡˈzæktli /

A1
  • adverb
  • No more and no less than; precisely

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

guess

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US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

whether

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US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

insight

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US / 'ɪnsaɪt /

UK / ˈɪnˌsaɪt /

B1
  • noun
  • Power to understand people and things very well
  • Very good understanding of something

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

show

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US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

cancel

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US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

else

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US / els /

UK / ɛls /

A1
  • adverb
  • Otherwise; if you fail to
  • (Of person place thing etc.) besides; in addition

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

possible

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US / ˈpɒsəbl /

UK / ˈpɑsəbəl /

A1
  • adjecitve
  • Being able or appropriate for a task or purpose
  • Having a chance of happening, or being true
  • Subtitles section
  • Solve for x, and we have the absolute value of 2x minus 5 is equal to 11.
  • Now, the big, I guess, insight you need to have whenever you have an absolute value equation like this is just to remember, if I have the absolute value of a is equal to 11, what do we know about a?
  • That means that a is equal to 11, or what else could a be?
  • Well, it could be negative 11.
  • a could be equal to negative 11 because there's two possible a's that are exactly 11 away from 0.
  • It could be positive 11 or it could be negative 11.
  • That's the exact same logic you apply in an equation like this.
  • If the absolute value of 2x minus 5 is equal to 11, that means that the stuff inside the absolute value sign either equals 11 or the stuff inside the absolute value sign is equal to negative 11.
  • Because if this is equal to 11, the absolute value of 11 is 11.
  • If this thing over here is equal to negative 11, when you take its absolute value, it'll still be equal to 11.
  • So let's write that down.
  • So 2x minus 5 could be equal to 11 or 2x minus 5 could be equal to negative 11, right?
  • Because in either case, if we took its absolute value, you would get 11.
  • Now, let's just solve each of these equations.
  • Over here, we can add 5 to both sides of this equation.
  • We get 11 plus 5 is 16.
  • 2x minus 5 plus 5 is just 2x.
  • 2x is equal to 16.
  • Divide both sides by 2, we get x is equal to 8.
  • Now, let's do this situation.
  • 2x minus 5 is equal to negative 11.
  • Let's add 5 to both sides of this equation.
  • The left-hand side we just get a 2x, the 5's cancel out.
  • 2x is equal to negative 5 plus 11, that's negative 6, and then we can divide both sides by 2.
  • And we get x is equal to negative 3.
  • So we've gotten two solutions depending on whether this thing in here is either equal to 11 or negative 11.
  • We got x could be equal to 8, in which case 2x minus 5 would be 11, or we have x is equal to negative 3, in which case 2x minus 5 is equal to negative 11.
  • Let's verify it.
  • So if x is equal to 8, let's show that it satisfies this equation.
  • So we'd get 2 times 8 minus 5.
  • The absolute value of 2 times 8 minus 5 should be equal to 11.
  • 2 times 8 is 16 minus 5 is 11, so we have the absolute value of 11, should be equal to 11.
  • And we know that's true.
  • The absolute value of 11 is 11.
  • So it all works out.
  • Now, let's try it with x is equal to negative 3.
  • We get the absolute value of 2 times negative 3 minus 5 should be equal to 11.
  • So what's 2 times negative 3?
  • 2 times negative 3 is negative 6 minus 5.
  • The absolute value of that should be equal to 11.
  • Well, negative 6 minus 5 is negative 11.
  • So the absolute value of negative 11 should be equal to 11, and it is.
  • The absolute value of negative 11 is 11.
  • So we get 11 is equal to 11.
  • So they both work.