Need up to 30 seconds to load.

what is the absolute value of five

and what is the absolute value of

negative eight

the absolute value of five is five

the absolute value of negative eight is

positive eight

the absolute value cannot produce a

negative result

it will always produce a positive result

or if you have 0 it will give you 0.

now let's say if you have an equation

for example the absolute value of x is

equal to seven

what are the possible values of x

x can equal two things seven

or negative seven because if you plug

these numbers in

the equation will be true

the absolute value of seven is seven so

this works the absolute value of

negative seven is also seven so

x could be seven or negative seven

both will make the equation true

so now how can we use this to solve a

typical problem

that involves an absolute value symbol

so let's say if we have the function

the absolute value of x plus 2 is equal

to 9.

how can we solve this equation

well the first thing you should do is

write two equations

the original one

and another one where the inside

function is equal

to negative nine instead of positive

nine and solve for both

so in the first one we can see that x

can be equal to seven

and for the second one

x

is equal to negative eleven

so these are the solutions

find the value of x

given this equation

so just like the last example let's set

2x minus 5

equal to 1

and negative one

so first let's add five

one plus five is six

and then let's divide both sides by two

so x is equal to three

and in the other example let's add five

to both sides negative 1 plus 5 is 4

and then divide by 2

x is 2.

so if you check the work

you can see that it's going to work out

so if we plug in two

two times two is four

four minus five is a negative one

the absolute value of negative one is

one

so the equation is true

now if we plug in three

it should also work

two times three

is equal to six

six minus five

is one

the absolute value of one is one

so that works

now what about this one

the absolute value of five x minus one

is equal to negative 2.

what's the solution

the absolute value function can never

equal

a negative number

so there's no solution for this

particular example

it can only equal zero or a positive

number

now let's try one more example for this

particular lesson

find the value of x

now what you don't want to do

is write this equation on the left is

equal to 7 or negative 7.

first you want to modify the equation

you want to get the absolute value

function

by itself

so let's add 2 first

so we're going to get 9

on the right side next let's divide by

3.

now you want the absolute value symbol

by itself on one side

once you have it at this point

now you want to write two equations

so the first one's gonna be x minus one

is equal to three

and the second x minus one is equal to

negative three

so if we add one

x is equal to four and if we add one to

the other one

negative three plus one is negative two

so this is the solution