Solve for x 2/3(9+x)=-5(4-x)

$\frac{2}{3} (9 + x) = - 5 (4 - x)$

Step 1

Simplify $\frac{2}{3} \cdot (9 + x)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (9 + x) = - 5 (4 - x)$

Simplify by adding zeros.

$\frac{2}{3} \cdot (9 + x) = - 5 (4 - x)$

Apply the distributive property.

$\frac{2}{3} \cdot 9 + \frac{2}{3} x = - 5 (4 - x)$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{2}{3} \cdot (3 (3)) + \frac{2}{3} x = - 5 (4 - x)$

Cancel the common factor.

$\frac{2}{3} \cdot (3 \cdot 3) + \frac{2}{3} x = - 5 (4 - x)$

Rewrite the expression.

$2 \cdot 3 + \frac{2}{3} x = - 5 (4 - x)$

Multiply $2$ by $3$ .

$6 + \frac{2}{3} x = - 5 (4 - x)$

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

$6 + \frac{2 x}{3} = - 5 (4 - x)$

Step 2

Simplify $- 5 (4 - x)$ .

Apply the distributive property.

$6 + \frac{2 x}{3} = - 5 \cdot 4 - 5 (- x)$

Multiply.

Multiply $- 5$ by $4$ .

$6 + \frac{2 x}{3} = - 20 - 5 (- x)$

Multiply $- 1$ by $- 5$ .

$6 + \frac{2 x}{3} = - 20 + 5 x$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$6 + \frac{2 x}{3} - 5 x = - 20$

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 + \frac{2 x}{3} - 5 x \cdot \frac{3}{3} = - 20$

Combine $- 5 x$ and $\frac{3}{3}$ .

$6 + \frac{2 x}{3} + \frac{- 5 x \cdot 3}{3} = - 20$

Combine the numerators over the common denominator.

$6 + \frac{2 x - 5 x \cdot 3}{3} = - 20$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x - 5 x \cdot 3$ .

Factor $x$ out of $2 x$ .

$6 + \frac{x \cdot 2 - 5 x \cdot 3}{3} = - 20$

Factor $x$ out of $- 5 x \cdot 3$ .

$6 + \frac{x \cdot 2 + x (- 5 \cdot 3)}{3} = - 20$

Factor $x$ out of $x \cdot 2 + x (- 5 \cdot 3)$ .

$6 + \frac{x (2 - 5 \cdot 3)}{3} = - 20$

Multiply $- 5$ by $3$ .

$6 + \frac{x (2 - 15)}{3} = - 20$

Subtract $15$ from $2$ .

$6 + \frac{x \cdot - 13}{3} = - 20$

Move $- 13$ to the left of $x$ .

$6 + \frac{- 13 \cdot x}{3} = - 20$

Move the negative in front of the fraction.

$6 - \frac{13 x}{3} = - 20$

Step 4

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

Subtract $6$ from both sides of the equation.

$- \frac{13 x}{3} = - 20 - 6$

Subtract $6$ from $- 20$ .

$- \frac{13 x}{3} = - 26$

Step 5

Multiply both sides of the equation by $- \frac{3}{13}$ .

$- \frac{3}{13} (- \frac{13 x}{3}) = - \frac{3}{13} \cdot - 26$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{13} (- \frac{13 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$\frac{- 3}{13} (- \frac{13 x}{3}) = - \frac{3}{13} \cdot - 26$

Move the leading negative in $- \frac{13 x}{3}$ into the numerator.

$\frac{- 3}{13} \cdot \frac{- 13 x}{3} = - \frac{3}{13} \cdot - 26$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{13} \cdot \frac{- 13 x}{3} = - \frac{3}{13} \cdot - 26$

Cancel the common factor.

$\frac{3 \cdot - 1}{13} \cdot \frac{- 13 x}{3} = - \frac{3}{13} \cdot - 26$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{3}{13} \cdot - 26$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{3}{13} \cdot - 26$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{3}{13} \cdot - 26$

Rewrite the expression.

$- - x = - \frac{3}{13} \cdot - 26$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{13} \cdot - 26$

Multiply $x$ by $1$ .

$x = - \frac{3}{13} \cdot - 26$

Simplify the right side.

Simplify $- \frac{3}{13} \cdot - 26$ .

Cancel the common factor of $13$ .

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$x = \frac{- 3}{13} \cdot - 26$

Factor $13$ out of $- 26$ .

$x = \frac{- 3}{13} \cdot (13 (- 2))$

Cancel the common factor.

$x = \frac{- 3}{13} \cdot (13 \cdot - 2)$

Rewrite the expression.

$x = - 3 \cdot - 2$

Multiply $- 3$ by $- 2$ .

$x = 6$

Solve for x 2/3(9+x)=-5(4-x)

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