Solve for x 1/15(2x+5)=(x+2)/9

$\frac{1}{15} (2 x + 5) = \frac{x + 2}{9}$

Step 1

Multiply both sides by $9$ .

$\frac{1}{15} \cdot (2 x + 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{1}{15} \cdot (2 x + 5) \cdot 9$ .

Apply the distributive property.

$(\frac{1}{15} (2 x) + \frac{1}{15} \cdot 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Multiply $\frac{1}{15} (2 x)$ .

Combine $2$ and $\frac{1}{15}$ .

$(\frac{2}{15} x + \frac{1}{15} \cdot 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Combine $\frac{2}{15}$ and $x$ .

$(\frac{2 x}{15} + \frac{1}{15} \cdot 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$(\frac{2 x}{15} + \frac{1}{5 (3)} \cdot 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Cancel the common factor.

$(\frac{2 x}{15} + \frac{1}{5 \cdot 3} \cdot 5) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Rewrite the expression.

$(\frac{2 x}{15} + \frac{1}{3}) \cdot 9 = \frac{x + 2}{9} \cdot 9$

Apply the distributive property.

$\frac{2 x}{15} \cdot 9 + \frac{1}{3} \cdot 9 = \frac{x + 2}{9} \cdot 9$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

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

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x}{5} \cdot 3 + \frac{1}{3} \cdot 9 = \frac{x + 2}{9} \cdot 9$

Combine $\frac{2 x}{5}$ and $3$ .

$\frac{2 x \cdot 3}{5} + \frac{1}{3} \cdot 9 = \frac{x + 2}{9} \cdot 9$

Multiply $3$ by $2$ .

$\frac{6 x}{5} + \frac{1}{3} \cdot 9 = \frac{x + 2}{9} \cdot 9$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{6 x}{5} + \frac{1}{3} \cdot (3 (3)) = \frac{x + 2}{9} \cdot 9$

Cancel the common factor.

$\frac{6 x}{5} + \frac{1}{3} \cdot (3 \cdot 3) = \frac{x + 2}{9} \cdot 9$

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $6 x - x \cdot 5$ .

Factor $x$ out of $6 x$ .

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

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

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

Factor $x$ out of $x \cdot 6 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{5} + 3 = 2$

Multiply $x$ by $1$ .

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

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $2$ .

$\frac{x}{5} = - 1$

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot - 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot - 1$

Rewrite the expression.

$x = 5 \cdot - 1$

Simplify the right side.

Multiply $5$ by $- 1$ .

$x = - 5$

Solve for x 1/15(2x+5)=(x+2)/9

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