Solve for x 9-(2x+7)/3=(x+5)/6

$9 - \frac{2 x + 7}{3} = \frac{x + 5}{6}$

Multiply both sides by $6$ .

$(9 - \frac{2 x + 7}{3}) \cdot 6 = \frac{x + 5}{6} \cdot 6$

Simplify.

Simplify the left side.

Simplify $(9 - \frac{2 x + 7}{3}) \cdot 6$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(9 \cdot \frac{3}{3} - \frac{2 x + 7}{3}) \cdot 6 = \frac{x + 5}{6} \cdot 6$

Simplify terms.

Combine $9$ and $\frac{3}{3}$ .

$(\frac{9 \cdot 3}{3} - \frac{2 x + 7}{3}) \cdot 6 = \frac{x + 5}{6} \cdot 6$

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - (2 x + 7)}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Simplify the numerator.

Multiply $9$ by $3$ .

$\frac{27 - (2 x + 7)}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Apply the distributive property.

$\frac{27 - (2 x) - 1 \cdot 7}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Multiply $2$ by $- 1$ .

$\frac{27 - 2 x - 1 \cdot 7}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Multiply $- 1$ by $7$ .

$\frac{27 - 2 x - 7}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Subtract $7$ from $27$ .

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

Factor $2$ out of $- 2 x + 20$ .

Factor $2$ out of $- 2 x$ .

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

Factor $2$ out of $20$ .

$\frac{2 (- x) + 2 (10)}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Factor $2$ out of $2 (- x) + 2 (10)$ .

$\frac{2 (- x + 10)}{3} \cdot 6 = \frac{x + 5}{6} \cdot 6$

Simplify terms.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{2 (- x + 10)}{3} \cdot (3 (2)) = \frac{x + 5}{6} \cdot 6$

Cancel the common factor.

$\frac{2 (- x + 10)}{3} \cdot (3 \cdot 2) = \frac{x + 5}{6} \cdot 6$

Rewrite the expression.

$2 (- x + 10) \cdot 2 = \frac{x + 5}{6} \cdot 6$

Multiply $2$ by $2$ .

$4 (- x + 10) = \frac{x + 5}{6} \cdot 6$

Apply the distributive property.

$4 (- x) + 4 \cdot 10 = \frac{x + 5}{6} \cdot 6$

Multiply.

Multiply $- 1$ by $4$ .

$- 4 x + 4 \cdot 10 = \frac{x + 5}{6} \cdot 6$

Multiply $4$ by $10$ .

$- 4 x + 40 = \frac{x + 5}{6} \cdot 6$

Simplify the right side.

Cancel the common factor of $6$ .

Cancel the common factor.

$- 4 x + 40 = \frac{x + 5}{6} \cdot 6$

Rewrite the expression.

$- 4 x + 40 = x + 5$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$- 4 x + 40 - x = 5$

Subtract $x$ from $- 4 x$ .

$- 5 x + 40 = 5$

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

Subtract $40$ from both sides of the equation.

$- 5 x = 5 - 40$

Subtract $40$ from $5$ .

$- 5 x = - 35$

Divide each term in $- 5 x = - 35$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 35$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 35}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 35}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 35}{- 5}$

Simplify the right side.

Divide $- 35$ by $- 5$ .

$x = 7$

Solve for x 9-(2x+7)/3=(x+5)/6

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