Answer
{-$\frac{1}{5}$}
Work Step by Step
2(4 - 3x) = 2(2x + 5)
Step 1 : Use distributive property
2.4- 2.(3x) = 2.(2x) + 2.5
simplify
8 - 6x = 4x +10
Step 2 : Collect variable terms on one side and constants on the other side.
subtract 4x from both the sides
8 - 6x - 4x = 4x + 10 -4x
Simplify
8 - 10x = 10
subtract 8 from both the sides
8 - 10x - 8 = 10 -8
Simplify
-10x = 2
Divide both the sides by -10
$\frac{-10x}{-10}$ = $\frac{2}{-10}$
x = $\frac{1}{-5}$
Now we check the proposed solution, -$\frac{1}{5}$ , by replacing x with -$\frac{1}{5}$ in the original equation.
Step 1: the original equation 2(4 - 3x) = 2(2x + 5)
Step2: Substitute -$\frac{1}{5}$ for x
2(4 - 3 .-$\frac{1}{5}$) = 2(2. -$\frac{1}{5}$ + 5)
Step 3: Multiply 3 .-$\frac{1}{5}$ = -$\frac{3}{5}$, 2. -$\frac{1}{5}$ = -$\frac{2}{5}$
2(4 + $\frac{3}{5}$) = 2(-$\frac{2}{5}$ + 5 )
Step 4: Solve
2($\frac{23}{5}$) = 2($\frac{23}{5}$)
$\frac{46}{5}$ = $\frac{46}{5}$
Since the check results in true statement, we conclude that the solution set of the given equation is {-$\frac{1}{5}$}
