Solve the Absolute Value Equation: |-4x| = 12

To solve the equation $\left|-4x\right|=12$, we consider the definition of absolute value:

1. The expression inside the absolute value can be either positive or negative, but its absolute value is always positive.

2. Therefore, we set up two equations to solve:

$-4x = 12$ and $-4x = -12$

3. Solving the first equation:

$-4x = 12$

4. Divide both sides by -4:

$x = -3$

5. Solving the second equation:

$-4x = -12$

6. Divide both sides by -4:

$x = 3$

7. Therefore, the solution is:

$x=-3$ , $x=3$