Answer
{$-\frac{19}{4},\frac{33}{4}$}
Work Step by Step
Using the rules for absolute values to generate two equations, we obtain:
Step 1: $|-4x+7|=26$
Step 2: $-4x+7=26$ and $-4x+7=-26$
Step 3: $-4x=26-7$ and $-4x=-26-7$
Step 4: $-4x=19$ and $-4x=-33$
Step 5: $x=\frac{19}{-4}$ and $x=\frac{-33}{-4}$
Step 6: $x=-\frac{19}{4}$ and $x=\frac{33}{4}$
Therefore, the solution set for the equation is {$-\frac{19}{4},\frac{33}{4}$}.
