Algebra Examples

$\frac{4}{5} \cdot x + x = 36$

Step 1

Simplify $\frac{4}{5} x + x$ .

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Step 1.1

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5} + x = 36$

Step 1.2

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

$\frac{4 x}{5} + x \cdot \frac{5}{5} = 36$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{4 x}{5} + \frac{x \cdot 5}{5} = 36$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{4 x + x \cdot 5}{5} = 36$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

$\frac{4 x + 5 \cdot x}{5} = 36$

Step 1.4.2

Add $4 x$ and $5 x$ .

$\frac{9 x}{5} = 36$

Step 2

Multiply both sides of the equation by $\frac{5}{9}$ .

$\frac{5}{9} \cdot \frac{9 x}{5} = \frac{5}{9} \cdot 36$

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 $\frac{5}{9} \cdot \frac{9 x}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{9 x}{5} = \frac{5}{9} \cdot 36$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{5}{9} \cdot 36$

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 $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{5}{9} \cdot 36$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{5}{9} \cdot 36$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{5}{9} \cdot 36$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{9} \cdot 36$ .

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Step 3.2.1.1

Cancel the common factor of $9$ .

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Step 3.2.1.1.1

Factor $9$ out of $36$ .

$x = \frac{5}{9} \cdot (9 (4))$

Step 3.2.1.1.2

Cancel the common factor.

$x = \frac{5}{9} \cdot (9 \cdot 4)$

Step 3.2.1.1.3

Rewrite the expression.

$x = 5 \cdot 4$

Step 3.2.1.2

Multiply $5$ by $4$ .

$x = 20$