Solve the Absolute Value Equation: |4x+1| = 9

To solve $\left|4x+1\right|=9$, split into two scenarios:

1) $4x+1=9$:

Subtract $1$ from both sides to get $4x=8$.

Divide both sides by $4$ to find $x=2$.

2) $4x+1=-9$:

Subtract $1$ from both sides to get $4x=-10$.

Divide both sides by $4$ to find $x=-2.5$.

Thus, $x=2$ and $x=-2.5$ are solutions.