Pre-Algebra Examples

$\frac{1}{4} x - \frac{3}{8} x = 4$

Step 1

Simplify $\frac{1}{4} x - \frac{3}{8} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - \frac{3}{8} x = 4$

Step 1.1.2

Combine $x$ and $\frac{3}{8}$ .

$\frac{x}{4} - \frac{x \cdot 3}{8} = 4$

Step 1.1.3

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

$\frac{x}{4} - \frac{3 x}{8} = 4$

Step 1.2

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

$\frac{x}{4} \cdot \frac{2}{2} - \frac{3 x}{8} = 4$

Step 1.3

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

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Step 1.3.1

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

$\frac{x \cdot 2}{4 \cdot 2} - \frac{3 x}{8} = 4$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{x \cdot 2}{8} - \frac{3 x}{8} = 4$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - 3 x}{8} = 4$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x - 3 x}{8} = 4$

Step 1.5.2

Subtract $3 x$ from $2 x$ .

$\frac{- x}{8} = 4$

Step 1.6

Move the negative in front of the fraction.

$- \frac{x}{8} = 4$

Step 2

Multiply both sides of the equation by $- 8$ .

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

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 $- 8 (- \frac{x}{8})$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{x}{8}$ into the numerator.

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

Step 3.1.1.1.2

Factor $8$ out of $- 8$ .

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

Step 3.1.1.1.3

Cancel the common factor.

$8 \cdot - 1 \frac{- x}{8} = - 8 \cdot 4$

Step 3.1.1.1.4

Rewrite the expression.

$- - x = - 8 \cdot 4$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 8 \cdot 4$

Step 3.1.1.2.2

Multiply $x$ by $1$ .

$x = - 8 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 8$ by $4$ .

$x = - 32$