Question

What is are the solutions to | x+4 |= 3x-5?

Answer 1

x =
`(9)/(2)`

Explanation:

The absolute value always returns a positive value but the expression inside can be positive or negative, that is

x + 4 = 3x - 5 ( subtract 3x from both sides )

- 2x + 4 = - 5 (subtract 4 from both sides )

- 2x = - 9 ( divide both sides by - 2 )

x =
`(9)/(2)`

OR

-(x + 4) = 3x - 5

- x - 4 = 3x - 5 ( subtract 3x from both sides )

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

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

x =
`(1)/(4)`

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

|
`(9)/(2)` + 4 | = |
`(17)/(2)` | =
`(17)/(2)`

right side =
`(27)/(2)` - 5 =
`(17)/(2)`

left side = right side , thus x =
`(9)/(2)` is a solution

check second solution

|
`(1)/(4)` + 4 | = |
`(17)/(4)` | =
`(17)/(4)`

right side =
`(3)/(4)` - 5 = -
`(17)/(4)`

right side ≠ left sides, hence not a solution