Pre-Algebra Examples

$\frac{2}{3} x - \frac{1}{9} x + 5 = 20$

Step 1

Simplify $\frac{2}{3} x - \frac{1}{9} x + 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 x}{3} - \frac{1}{9} x + 5 = 20$

Step 1.1.2

Combine $x$ and $\frac{1}{9}$ .

$\frac{2 x}{3} - \frac{x}{9} + 5 = 20$

Step 1.2

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

$\frac{2 x}{3} \cdot \frac{3}{3} - \frac{x}{9} + 5 = 20$

Step 1.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

$\frac{2 x \cdot 3}{3 \cdot 3} - \frac{x}{9} + 5 = 20$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{2 x \cdot 3}{9} - \frac{x}{9} + 5 = 20$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - x}{9} + 5 = 20$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

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

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Step 1.5.1.1.1

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

$\frac{x (2 \cdot 3) - x}{9} + 5 = 20$

Step 1.5.1.1.2

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 3) + x \cdot - 1}{9} + 5 = 20$

Step 1.5.1.1.3

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

$\frac{x (2 \cdot 3 - 1)}{9} + 5 = 20$

Step 1.5.1.2

Multiply $2$ by $3$ .

$\frac{x (6 - 1)}{9} + 5 = 20$

Step 1.5.1.3

Subtract $1$ from $6$ .

$\frac{x \cdot 5}{9} + 5 = 20$

Step 1.5.2

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

$\frac{5 x}{9} + 5 = 20$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{5 x}{9} = 20 - 5$

Step 2.2

Subtract $5$ from $20$ .

$\frac{5 x}{9} = 15$

Step 3

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

$\frac{9}{5} \cdot \frac{5 x}{9} = \frac{9}{5} \cdot 15$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 x}{9} = \frac{9}{5} \cdot 15$

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{9}{5} \cdot 15$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{9}{5} \cdot 15$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Factor $5$ out of $15$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$x = 9 \cdot 3$

Step 4.2.1.2

Multiply $9$ by $3$ .

$x = 27$