Pre-Algebra Examples

$\frac{2}{5} x - \frac{3}{10} x = 2$

Step 1

Simplify $\frac{2}{5} x - \frac{3}{10} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 x}{5} - \frac{3}{10} x = 2$

Step 1.1.2

Combine $x$ and $\frac{3}{10}$ .

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

Step 1.1.3

Move $3$ to the left of $x$ .

$\frac{2 x}{5} - \frac{3 x}{10} = 2$

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{2 x \cdot 2}{10} - \frac{3 x}{10} = 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - 3 x}{10} = 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

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Step 1.5.1.1

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

$\frac{x (2 \cdot 2) - 3 x}{10} = 2$

Step 1.5.1.2

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

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

Step 1.5.1.3

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

$\frac{x (2 \cdot 2 - 3)}{10} = 2$

Step 1.5.2

Multiply $2$ by $2$ .

$\frac{x (4 - 3)}{10} = 2$

Step 1.5.3

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{10} = 2$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{10} = 2$

Step 2

Multiply both sides of the equation by $10$ .

$10 \frac{x}{10} = 10 \cdot 2$

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 $10$ .

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Step 3.1.1.1

Cancel the common factor.

$10 \frac{x}{10} = 10 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$x = 10 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $10$ by $2$ .

$x = 20$