Solve the Absolute Value Equation: |3x| = 21

To solve the equation $\left|3x\right|=21$, 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:

$3x = 21$ and $3x = -21$

3. Solving the first equation:

$3x = 21$

4. Divide both sides by 3:

$x = 7$

5. Solving the second equation:

$3x = -21$

6. Divide both sides by 3:

$x = -7$

7. Therefore, the solution is:

$x=-7$ , $x=7$