Algebra Examples

$\frac{12}{5} x - 2 x = \frac{3}{10}$

Step 1

Simplify $\frac{12}{5} x - 2 x$ .

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Step 1.1

Combine $\frac{12}{5}$ and $x$ .

$\frac{12 x}{5} - 2 x = \frac{3}{10}$

Step 1.2

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

$\frac{12 x}{5} - 2 x \cdot \frac{5}{5} = \frac{3}{10}$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{12 x}{5} + \frac{- 2 x \cdot 5}{5} = \frac{3}{10}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{12 x - 2 x \cdot 5}{5} = \frac{3}{10}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $2 x$ out of $12 x - 2 x \cdot 5$ .

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Step 1.4.1.1

Factor $2 x$ out of $12 x$ .

$\frac{2 x (6) - 2 x \cdot 5}{5} = \frac{3}{10}$

Step 1.4.1.2

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

$\frac{2 x (6) + 2 x (- 1 \cdot 5)}{5} = \frac{3}{10}$

Step 1.4.1.3

Factor $2 x$ out of $2 x (6) + 2 x (- 1 \cdot 5)$ .

$\frac{2 x (6 - 1 \cdot 5)}{5} = \frac{3}{10}$

Step 1.4.2

Multiply $- 1$ by $5$ .

$\frac{2 x (6 - 5)}{5} = \frac{3}{10}$

Step 1.4.3

Subtract $5$ from $6$ .

$\frac{2 x \cdot 1}{5} = \frac{3}{10}$

Step 1.4.4

Multiply $2$ by $1$ .

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

Step 2

Multiply both sides of the equation by $\frac{5}{2}$ .

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

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 $\frac{5}{2} \cdot \frac{2 x}{5}$ .

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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.

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

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot \frac{3}{10}$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{5}{2} \cdot \frac{3}{10}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot \frac{3}{10}$

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{2} \cdot \frac{3}{10}$ .

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Factor $5$ out of $10$ .

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

Step 3.2.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.3

Rewrite the expression.

$x = \frac{1}{2} \cdot \frac{3}{2}$

Step 3.2.1.2

Multiply $\frac{1}{2}$ by $\frac{3}{2}$ .

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

Step 3.2.1.3

Multiply $2$ by $2$ .

$x = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$