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

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

Simplify $\frac{x + 2}{9} - \frac{2 x + 9}{5}$ .

To write $\frac{x + 2}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

To write $- \frac{2 x + 9}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 2}{9}$ by $\frac{5}{5}$ .

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

Multiply $9$ by $5$ .

$\frac{(x + 2) \cdot 5}{45} - \frac{2 x + 9}{5} \cdot \frac{9}{9} = 2 x + 3$

Multiply $\frac{2 x + 9}{5}$ by $\frac{9}{9}$ .

$\frac{(x + 2) \cdot 5}{45} - \frac{(2 x + 9) \cdot 9}{5 \cdot 9} = 2 x + 3$

Multiply $5$ by $9$ .

$\frac{(x + 2) \cdot 5}{45} - \frac{(2 x + 9) \cdot 9}{45} = 2 x + 3$

Combine the numerators over the common denominator.

$\frac{(x + 2) \cdot 5 - (2 x + 9) \cdot 9}{45} = 2 x + 3$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 5 + 2 \cdot 5 - (2 x + 9) \cdot 9}{45} = 2 x + 3$

Move $5$ to the left of $x$ .

$\frac{5 \cdot x + 2 \cdot 5 - (2 x + 9) \cdot 9}{45} = 2 x + 3$

Multiply $2$ by $5$ .

$\frac{5 \cdot x + 10 - (2 x + 9) \cdot 9}{45} = 2 x + 3$

Apply the distributive property.

$\frac{5 x + 10 + (- (2 x) - 1 \cdot 9) \cdot 9}{45} = 2 x + 3$

Multiply $2$ by $- 1$ .

$\frac{5 x + 10 + (- 2 x - 1 \cdot 9) \cdot 9}{45} = 2 x + 3$

Multiply $- 1$ by $9$ .

$\frac{5 x + 10 + (- 2 x - 9) \cdot 9}{45} = 2 x + 3$

Apply the distributive property.

$\frac{5 x + 10 - 2 x \cdot 9 - 9 \cdot 9}{45} = 2 x + 3$

Multiply $9$ by $- 2$ .

$\frac{5 x + 10 - 18 x - 9 \cdot 9}{45} = 2 x + 3$

Multiply $- 9$ by $9$ .

$\frac{5 x + 10 - 18 x - 81}{45} = 2 x + 3$

Subtract $18 x$ from $5 x$ .

$\frac{- 13 x + 10 - 81}{45} = 2 x + 3$

Subtract $81$ from $10$ .

$\frac{- 13 x - 71}{45} = 2 x + 3$

Simplify with factoring out.

Factor $- 1$ out of $- 13 x$ .

$\frac{- (13 x) - 71}{45} = 2 x + 3$

Rewrite $- 71$ as $- 1 (71)$ .

$\frac{- (13 x) - 1 (71)}{45} = 2 x + 3$

Factor $- 1$ out of $- (13 x) - 1 (71)$ .

$\frac{- (13 x + 71)}{45} = 2 x + 3$

Simplify the expression.

Rewrite $- (13 x + 71)$ as $- 1 (13 x + 71)$ .

$\frac{- 1 (13 x + 71)}{45} = 2 x + 3$

Move the negative in front of the fraction.

$- \frac{13 x + 71}{45} = 2 x + 3$

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

Subtract $2 x$ from both sides of the equation.

$- \frac{13 x + 71}{45} - 2 x = 3$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{45}{45}$ .

$- \frac{13 x + 71}{45} - 2 x \cdot \frac{45}{45} = 3$

Combine $- 2 x$ and $\frac{45}{45}$ .

$- \frac{13 x + 71}{45} + \frac{- 2 x \cdot 45}{45} = 3$

Combine the numerators over the common denominator.

$\frac{- (13 x + 71) - 2 x \cdot 45}{45} = 3$

Simplify the numerator.

Apply the distributive property.

$\frac{- (13 x) - 1 \cdot 71 - 2 x \cdot 45}{45} = 3$

Multiply $13$ by $- 1$ .

$\frac{- 13 x - 1 \cdot 71 - 2 x \cdot 45}{45} = 3$

Multiply $- 1$ by $71$ .

$\frac{- 13 x - 71 - 2 x \cdot 45}{45} = 3$

Multiply $45$ by $- 2$ .

$\frac{- 13 x - 71 - 90 x}{45} = 3$

Subtract $90 x$ from $- 13 x$ .

$\frac{- 103 x - 71}{45} = 3$

Factor $- 1$ out of $- 103 x$ .

$\frac{- (103 x) - 71}{45} = 3$

Rewrite $- 71$ as $- 1 (71)$ .

$\frac{- (103 x) - 1 (71)}{45} = 3$

Factor $- 1$ out of $- (103 x) - 1 (71)$ .

$\frac{- (103 x + 71)}{45} = 3$

Rewrite $- (103 x + 71)$ as $- 1 (103 x + 71)$ .

$\frac{- 1 (103 x + 71)}{45} = 3$

Move the negative in front of the fraction.

$- \frac{103 x + 71}{45} = 3$

Multiply both sides of the equation by $- 45$ .

$- 45 (- \frac{103 x + 71}{45}) = - 45 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 45 (- \frac{103 x + 71}{45})$ .

Cancel the common factor of $45$ .

Move the leading negative in $- \frac{103 x + 71}{45}$ into the numerator.

$- 45 \frac{- (103 x + 71)}{45} = - 45 \cdot 3$

Factor $45$ out of $- 45$ .

$45 (- 1) \frac{- (103 x + 71)}{45} = - 45 \cdot 3$

Cancel the common factor.

$45 \cdot - 1 \frac{- (103 x + 71)}{45} = - 45 \cdot 3$

Rewrite the expression.

$- - (103 x + 71) = - 45 \cdot 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (103 x + 71) = - 45 \cdot 3$

Multiply $103 x + 71$ by $1$ .

$103 x + 71 = - 45 \cdot 3$

Simplify the right side.

Multiply $- 45$ by $3$ .

$103 x + 71 = - 135$

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

Subtract $71$ from both sides of the equation.

$103 x = - 135 - 71$

Subtract $71$ from $- 135$ .

$103 x = - 206$

Divide each term in $103 x = - 206$ by $103$ and simplify.

Divide each term in $103 x = - 206$ by $103$ .

$\frac{103 x}{103} = \frac{- 206}{103}$

Simplify the left side.

Cancel the common factor of $103$ .

Cancel the common factor.

$\frac{103 x}{103} = \frac{- 206}{103}$

Divide $x$ by $1$ .

$x = \frac{- 206}{103}$

Simplify the right side.

Divide $- 206$ by $103$ .

$x = - 2$

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

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