Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

Combine $x$ and $\frac{1}{3}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

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

Step 1.4.2

Multiply $5$ by $3$ .

$\frac{2 x \cdot 3}{15} - \frac{x}{3} \cdot \frac{5}{5} = 2$

Step 1.4.3

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

$\frac{2 x \cdot 3}{15} - \frac{x \cdot 5}{3 \cdot 5} = 2$

Step 1.4.4

Multiply $3$ by $5$ .

$\frac{2 x \cdot 3}{15} - \frac{x \cdot 5}{15} = 2$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - x \cdot 5}{15} = 2$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $x$ out of $2 x \cdot 3 - x \cdot 5$ .

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Step 1.6.1.1

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

$\frac{x (2 \cdot 3) - x \cdot 5}{15} = 2$

Step 1.6.1.2

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

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

Step 1.6.1.3

Factor $x$ out of $x (2 \cdot 3) + x (- 1 \cdot 5)$ .

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

Step 1.6.2

Multiply $2$ by $3$ .

$\frac{x (6 - 1 \cdot 5)}{15} = 2$

Step 1.6.3

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{15} = 2$

Step 1.6.4

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{15} = 2$

Step 1.7

Multiply $x$ by $1$ .

$\frac{x}{15} = 2$

Step 2

Multiply both sides of the equation by $15$ .

$15 \frac{x}{15} = 15 \cdot 2$

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

Cancel the common factor of $15$ .

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Step 3.1.1.1

Cancel the common factor.

$15 \frac{x}{15} = 15 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$x = 15 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $15$ by $2$ .

$x = 30$