#### Answer

{-17}

#### Work Step by Step

4x -14 = -82
Step 1: Add 14 on both the sides
4x -14 +14 = -82 +14
Step 2: Simplify
4x = -68
Step 3: Divide both the sides by 4
$\frac{4x}{4}$ = $\frac{-68}{4}$
Step 4: Simplify
x = -17
Now we check the proposed solution, -17, by replacing x with -17 in the original equation.
Step 1: the original equation 4x -14 = -82
Step2: Substitute -17 for x
4.(-17) - 14 =-82
Step 3: Multiply 4.(-17) = -68
-68 - 14 = -82
Step 4: Solve -68 - 14 = -82
-82 =-82
Since the check results in true statement, we conclude that the solution set of the given equation is {-17}