Pre-Algebra Examples

$\frac{5}{8} x = \frac{1}{2} x + 2$

Step 1

Simplify $\frac{5}{8} x$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{5}{8} x = \frac{1}{2} x + 2$

Step 1.2

Simplify by adding zeros.

$\frac{5}{8} x = \frac{1}{2} x + 2$

Step 1.3

Combine $\frac{5}{8}$ and $x$ .

$\frac{5 x}{8} = \frac{1}{2} x + 2$

Step 2

Combine $\frac{1}{2}$ and $x$ .

$\frac{5 x}{8} = \frac{x}{2} + 2$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{5 x}{8} - \frac{x}{2} = 2$

Step 3.2

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

$\frac{5 x}{8} - \frac{x}{2} \cdot \frac{4}{4} = 2$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

$\frac{5 x}{8} - \frac{x \cdot 4}{2 \cdot 4} = 2$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{5 x}{8} - \frac{x \cdot 4}{8} = 2$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 x - x \cdot 4}{8} = 2$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $x$ out of $5 x - x \cdot 4$ .

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Step 3.5.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - x \cdot 4}{8} = 2$

Step 3.5.1.2

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

$\frac{x \cdot 5 + x (- 1 \cdot 4)}{8} = 2$

Step 3.5.1.3

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 4)$ .

$\frac{x (5 - 1 \cdot 4)}{8} = 2$

Step 3.5.2

Multiply $- 1$ by $4$ .

$\frac{x (5 - 4)}{8} = 2$

Step 3.5.3

Subtract $4$ from $5$ .

$\frac{x \cdot 1}{8} = 2$

Step 3.6

Multiply $x$ by $1$ .

$\frac{x}{8} = 2$

Step 4

Multiply both sides of the equation by $8$ .

$8 \frac{x}{8} = 8 \cdot 2$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1

Cancel the common factor.

$8 \frac{x}{8} = 8 \cdot 2$

Step 5.1.1.2

Rewrite the expression.

$x = 8 \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $8$ by $2$ .

$x = 16$