Algebra Examples

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

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.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Factor $5$ out of $15$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Apply the distributive property.

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

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Factor $3$ out of $15$ .

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

Step 2.1.1.5.2

Factor $3$ out of $9$ .

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

Step 2.1.1.5.3

Cancel the common factor.

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

Step 2.1.1.5.4

Rewrite the expression.

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

Step 2.1.1.6

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

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

Step 2.1.1.7

Multiply $3$ by $2$ .

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

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

Factor $3$ out of $9$ .

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

Step 2.1.1.8.2

Cancel the common factor.

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

Step 2.1.1.8.3

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

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

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Step 3.1.5.1.1.1

Factor $x$ out of $6 x$ .

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

Step 3.1.5.1.1.2

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

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

Step 3.1.5.1.1.3

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

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

Step 3.1.5.1.2

Multiply $- 1$ by $5$ .

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

Step 3.1.5.1.3

Subtract $5$ from $6$ .

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

Step 3.1.5.2

Multiply $x$ by $1$ .

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

Step 3.2

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

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Step 3.2.1

Subtract $3$ from both sides of the equation.

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

Step 3.2.2

Subtract $3$ from $2$ .

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

Step 3.3

Multiply both sides of the equation by $5$ .

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

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Cancel the common factor of $5$ .

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Step 3.4.1.1.1

Cancel the common factor.

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

Step 3.4.1.1.2

Rewrite the expression.

$x = 5 \cdot - 1$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $5$ by $- 1$ .

$x = - 5$