#### Answer

{5}

#### Work Step by Step

3(x + 1) = 7(x - 2) - 3
Step 1 : Use distributive property
3.x + 3 = 7.x - 7.2 - 3
simplify
3x + 3 = 7x - 14 - 3
3x +3 = 7x -17
Step 2 : Collect variable terms on one side and constants on the other side.
subtract 7x from both the sides
3x + 3 - 7x = 7x -17 -7x
simplify
-4x + 3 = -17
subtract 3 from both the sides
-4x +3 - 3 = -17 -3
-4x = -20
Divide both the sides by -4
$\frac{-4x}{-4}$ = $\frac{-20}{-4}$
x = 5
Now we check the proposed solution, 5 , by replacing x with 5 in the original equation.
Step 1: the original equation 3(x + 1) = 7(x - 2) - 3
Step2: Substitute 5 for x
3(5 + 1) = 7(5 - 2) - 3
Step 4: Solve
3(6) = 7(3) - 3
Multiply 3(6) = 3.6 = 18, 7(3)= 7.3 = 21
18 = 21 -3
18 = 18
Since the check results in true statement, we conclude that the solution set of the given equation is {5}