Answer
{$-\frac{15}{2},6$}
Work Step by Step
Using the rules for absolute values to generate two equations, we obtain:
Step 1: $|4x+3|=27$
Step 2: $4x+3=27$ and $4x+3=-27$
Step 3: $4x=27-3$ and $4x=-27-3$
Step 4: $4x=24$ and $4x=-30$
Step 5: $x=\frac{24}{4}$ and $x=-\frac{30}{4}$
Step 6: $x=6$ and $x=-\frac{15}{2}$
Therefore, the solution set for the equation is {$-\frac{15}{2},6$}.
