Answer
{$-\frac{7}{4},-\frac{3}{4}$}
Work Step by Step
Using the rules for absolute values to generate two equations, we obtain:
Step 1: $|4x+5|=2$
Step 2: $4x+5=2$ and $4x+5=-2$
Step 3: $4x=2-5$ and $4x=-2-5$
Step 4: $4x=-3$ and $4x=-7$
Step 5: $x=-\frac{3}{4}$ and $x=-\frac{7}{4}$
Therefore, the solution set for the equation is {$-\frac{7}{4},-\frac{3}{4}$}.
