#### Answer

{6}

#### Work Step by Step

5(2x - 8) - 2 = 5(x - 3) + 3
Step 1 : Use distributive property
5.2x -5.8 -2 = 5.x -5.3 + 3
Multiply
10x -40 - 2 = 5x -15 +3
Solve
10x -42 = 5x -12
Step 2 : Collect variable terms on one side and constants on the other side.
subtract 5x from both the sides
10x - 42 -5x = 5x -12 - 5x
5x - 42 = -12
Add 42 on both the sides
5x - 42 + 42 = -12 + 42
5x = 30
Divide both the sides by 5
$\frac{5x}{5}$ = $\frac{30}{5}$
x = 6
Now we check the proposed solution, 6 , by replacing x with 6 in the original equation.
Step 1: the original equation 5(2x - 8) - 2 = 5(x - 3) + 3
Step2: Substitute 6 for x
5(2.6 - 8) - 2 = 5(6 - 3) + 3
Step 3: Simplify
5(12 - 8) - 2 = 5(3) + 3
5(4) -2 = 5(3) + 3
Multiply 5(4) = 5.4 = 20, 5(3) = 5.3 = 15
20 - 2 = 15 + 3
Solve
18 = 18
Since the check results in true statement, we conclude that the solution set of the given equation is {6}