Solve for x (2(x+4))/3-8=32

$\frac{2 (x + 4)}{3} - 8 = 32$

Step 1

Simplify $\frac{2 (x + 4)}{3} - 8$ .

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 (x + 4)}{3} - 8 \cdot \frac{3}{3} = 32$

Simplify terms.

Combine $- 8$ and $\frac{3}{3}$ .

$\frac{2 (x + 4)}{3} + \frac{- 8 \cdot 3}{3} = 32$

Combine the numerators over the common denominator.

$\frac{2 (x + 4) - 8 \cdot 3}{3} = 32$

Simplify the numerator.

Factor $2$ out of $2 (x + 4) - 8 \cdot 3$ .

Factor $2$ out of $- 8 \cdot 3$ .

$\frac{2 (x + 4) + 2 (- 4 \cdot 3)}{3} = 32$

Factor $2$ out of $2 (x + 4) + 2 (- 4 \cdot 3)$ .

$\frac{2 (x + 4 - 4 \cdot 3)}{3} = 32$

Multiply $- 4$ by $3$ .

$\frac{2 (x + 4 - 12)}{3} = 32$

Subtract $12$ from $4$ .

$\frac{2 (x - 8)}{3} = 32$

Step 2

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 (x - 8)}{3} = \frac{3}{2} \cdot 32$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 (x - 8)}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 (x - 8)}{3} = \frac{3}{2} \cdot 32$

Rewrite the expression.

$\frac{1}{2} (2 (x - 8)) = \frac{3}{2} \cdot 32$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} (2 (x - 8)) = \frac{3}{2} \cdot 32$

Rewrite the expression.

$x - 8 = \frac{3}{2} \cdot 32$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 32$ .

Cancel the common factor of $2$ .

Factor $2$ out of $32$ .

$x - 8 = \frac{3}{2} \cdot (2 (16))$

Cancel the common factor.

$x - 8 = \frac{3}{2} \cdot (2 \cdot 16)$

Rewrite the expression.

$x - 8 = 3 \cdot 16$

Multiply $3$ by $16$ .

$x - 8 = 48$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$x = 48 + 8$

Add $48$ and $8$ .

$x = 56$

Solve for x (2(x+4))/3-8=32

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