Question

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

Answer 1

Answer:

x = $\frac{9}{2}$

Step-by-step 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 = $\frac{9}{2}$

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 = $\frac{1}{4}$

As a check

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

| $\frac{9}{2}$ + 4 | = | $\frac{17}{2}$ | = $\frac{17}{2}$

right side = $\frac{27}{2}$ - 5 = $\frac{17}{2}$

left side = right side , thus x = $\frac{9}{2}$ is a solution

check second solution

| $\frac{1}{4}$ + 4 | = |  $\frac{17}{4}$ | = $\frac{17}{4}$

right side =   $\frac{3}{4}$ - 5 = -   $\frac{17}{4}$

right side ≠ left sides, hence not a solution