Pre-Algebra Examples

$\frac{2}{3} x - \frac{7}{12} x = 2$

Step 1

Simplify $\frac{2}{3} x - \frac{7}{12} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 x}{3} - \frac{7}{12} x = 2$

Step 1.1.2

Combine $x$ and $\frac{7}{12}$ .

$\frac{2 x}{3} - \frac{x \cdot 7}{12} = 2$

Step 1.1.3

Move $7$ to the left of $x$ .

$\frac{2 x}{3} - \frac{7 x}{12} = 2$

Step 1.2

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x}{3} \cdot \frac{4}{4} - \frac{7 x}{12} = 2$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2 x}{3}$ by $\frac{4}{4}$ .

$\frac{2 x \cdot 4}{3 \cdot 4} - \frac{7 x}{12} = 2$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{2 x \cdot 4}{12} - \frac{7 x}{12} = 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 4 - 7 x}{12} = 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $2 x \cdot 4 - 7 x$ .

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Step 1.5.1.1

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x (2 \cdot 4) - 7 x}{12} = 2$

Step 1.5.1.2

Factor $x$ out of $- 7 x$ .

$\frac{x (2 \cdot 4) + x \cdot - 7}{12} = 2$

Step 1.5.1.3

Factor $x$ out of $x (2 \cdot 4) + x \cdot - 7$ .

$\frac{x (2 \cdot 4 - 7)}{12} = 2$

Step 1.5.2

Multiply $2$ by $4$ .

$\frac{x (8 - 7)}{12} = 2$

Step 1.5.3

Subtract $7$ from $8$ .

$\frac{x \cdot 1}{12} = 2$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{12} = 2$

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{x}{12} = 12 \cdot 2$

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 $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{x}{12} = 12 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$x = 12 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $12$ by $2$ .

$x = 24$