Pre-Algebra Examples

$\frac{3 x}{10} + \frac{3 x}{5} = 9$

Step 1

Simplify $\frac{3 x}{10} + \frac{3 x}{5}$ .

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Step 1.1

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{3 x}{5}$ by $\frac{2}{2}$ .

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

Step 1.2.2

Multiply $5$ by $2$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $3 x$ out of $3 x + 3 x \cdot 2$ .

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Step 1.4.1.1

Factor $3 x$ out of $3 x$ .

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

Step 1.4.1.2

Factor $3 x$ out of $3 x \cdot 2$ .

$\frac{3 x (1) + 3 x (2)}{10} = 9$

Step 1.4.1.3

Factor $3 x$ out of $3 x (1) + 3 x (2)$ .

$\frac{3 x (1 + 2)}{10} = 9$

Step 1.4.2

Add $1$ and $2$ .

$\frac{3 x \cdot 3}{10} = 9$

Step 1.4.3

Multiply $3$ by $3$ .

$\frac{9 x}{10} = 9$

Step 2

Multiply both sides of the equation by $\frac{10}{9}$ .

$\frac{10}{9} \cdot \frac{9 x}{10} = \frac{10}{9} \cdot 9$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{10}{9} \cdot \frac{9 x}{10}$ .

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Step 3.1.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{10}{9} \cdot \frac{9 x}{10} = \frac{10}{9} \cdot 9$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{10}{9} \cdot 9$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{10}{9} \cdot 9$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{10}{9} \cdot 9$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{10}{9} \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$x = \frac{10}{9} \cdot 9$

Step 3.2.1.2

Rewrite the expression.

$x = 10$