Question

Solve for all values of X in simplest form |4x-4|-8=-3

Answer 1

x = -
`(1)/(4)` , x =
`(9)/(4)`

Explanation:

| 4x - 4 | - 8 = - 3 ( add 8 to both sides )

| 4x - 4 | = 5

the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, then

4x - 4 = 5 or - (4x - 4) = 5 , have to be solved

4x - 4 = 5 ( add 4 to both sides )

4x = 9 ( divide both sides by 4 )

x =
`(9)/(4)`

or

- (4x - 4) = 5

- 4x + 4 = 5 ( subtract 4 from both sides )

- 4x = 1 ( divide both sides by - 4 )

x = -
`(1)/(4)`

As a check

substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = -
`(1)/(4)`

| 4(-
`(1)/(4)` ) - 4 | - 8 = | - 1 - 4 | - 8 = | - 5 | - 8 = 5 - 8 = - 3 = right side

x =
`(9)/(4)`

| 4 (
`(9)/(4)` ) - 4 | - 8 = | 9 - 4 | - 8 = | 5 | - 8 = 5 - 8 = - 3 = right side

then x = -
`(1)/(4)` , x =
`(9)/(4)` are the solutions