#### Answer

{-7}

#### Work Step by Step

9x -14 = -77
Step 1: Add 14 on both the sides
9x - 14 +14 = -77 +14
Step 2: Simplify
9x = -63
Step 3: Divide both the sides by 9
$\frac{9x}{9}$ = $\frac{-63}{9}$
Step 4: Simplify
x = -7
Now we check the proposed solution, -7, by replacing x with -7 in the original equation.
Step 1: the original equation 9x -14 =-77
Step2: Substitute -7 for x
9.(-7) - 14 = -77
Step 3: Multiply 9.(-7) = -63
-63 - 14 = -77
Step 4: Solve -63 -14 = -77
-77 =-77
Since the check results in true statement, we conclude that the solution set of the given equation is {-7}