Solve the Absolute Value Equation: |2x+3| = 9

To solve the equation $\left|2x+3\right|=9$, we split it into two separate equations:

1. $2x+3=9$

2. $2x+3=-9$

For the first equation:

$2x+3=9$

Subtract 3 from both sides:

$2x=6$

Divide both sides by 2:

$x=3$

For the second equation:

$2x+3=-9$

Subtract 3 from both sides:

$2x=-12$

Divide both sides by 2:

$x=-6$

Thus, the solutions are $x=3$ and $x=-6$.