Solve for x 2/3*(x-12)=x+8

$\frac{2}{3} \cdot (x - 12) = x + 8$

Step 1

Simplify $\frac{2}{3} \cdot (x - 12)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (x - 12) = x + 8$

Simplify by adding zeros.

$\frac{2}{3} \cdot (x - 12) = x + 8$

Apply the distributive property.

$\frac{2}{3} x + \frac{2}{3} \cdot - 12 = x + 8$

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} + \frac{2}{3} \cdot - 12 = x + 8$

Cancel the common factor of $3$ .

Factor $3$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 4$ .

$\frac{2 x}{3} - 8 = x + 8$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $2 x$ .

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

Factor $x$ out of $- x \cdot 3$ .

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

Factor $x$ out of $x \cdot 2 + x (- 1 \cdot 3)$ .

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

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $2$ .

$\frac{x \cdot - 1}{3} - 8 = 8$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{3} - 8 = 8$

Move the negative in front of the fraction.

$- \frac{x}{3} - 8 = 8$

Step 3

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

Add $8$ to both sides of the equation.

$- \frac{x}{3} = 8 + 8$

Add $8$ and $8$ .

$- \frac{x}{3} = 16$

Step 4

Multiply both sides of the equation by $- 3$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 \cdot 16$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 \cdot 16$

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 \cdot 16$

Rewrite the expression.

$- - x = - 3 \cdot 16$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot 16$

Multiply $x$ by $1$ .

$x = - 3 \cdot 16$

Simplify the right side.

Multiply $- 3$ by $16$ .

$x = - 48$

Solve for x 2/3*(x-12)=x+8

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