Solve for x 7x-22=-1/3(9x+6)

$7 x - 22 = - \frac{1}{3} (9 x + 6)$

Step 1

Simplify $- \frac{1}{3} \cdot (9 x + 6)$ .

Rewrite.

$7 x - 22 = 0 + 0 - \frac{1}{3} \cdot (9 x + 6)$

Simplify by adding zeros.

$7 x - 22 = - \frac{1}{3} \cdot (9 x + 6)$

Apply the distributive property.

$7 x - 22 = - \frac{1}{3} (9 x) - \frac{1}{3} \cdot 6$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$7 x - 22 = \frac{- 1}{3} (9 x) - \frac{1}{3} \cdot 6$

Factor $3$ out of $9 x$ .

$7 x - 22 = \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot 6$

Cancel the common factor.

$7 x - 22 = \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot 6$

Rewrite the expression.

$7 x - 22 = - 1 (3 x) - \frac{1}{3} \cdot 6$

Multiply $3$ by $- 1$ .

$7 x - 22 = - 3 x - \frac{1}{3} \cdot 6$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$7 x - 22 = - 3 x + \frac{- 1}{3} \cdot 6$

Factor $3$ out of $6$ .

$7 x - 22 = - 3 x + \frac{- 1}{3} \cdot (3 (2))$

Cancel the common factor.

$7 x - 22 = - 3 x + \frac{- 1}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$7 x - 22 = - 3 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$7 x - 22 = - 3 x - 2$

Step 2

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

Add $3 x$ to both sides of the equation.

$7 x - 22 + 3 x = - 2$

Add $7 x$ and $3 x$ .

$10 x - 22 = - 2$

Step 3

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

Add $22$ to both sides of the equation.

$10 x = - 2 + 22$

Add $- 2$ and $22$ .

$10 x = 20$

Step 4

Divide each term in $10 x = 20$ by $10$ and simplify.

Divide each term in $10 x = 20$ by $10$ .

$\frac{10 x}{10} = \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{20}{10}$

Divide $x$ by $1$ .

$x = \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$x = 2$

Solve for x 7x-22=-1/3(9x+6)

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