Pre-Algebra Examples

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

Step 1

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 = (x - 1 + \frac{3}{8}) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x}{4} \cdot 4 = (x - 1 + \frac{3}{8}) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$x = (x - 1 + \frac{3}{8}) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 1 + \frac{3}{8}) \cdot 4$ .

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Step 2.2.1.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = (x - 1 \cdot \frac{8}{8} + \frac{3}{8}) \cdot 4$

Step 2.2.1.2

Combine $- 1$ and $\frac{8}{8}$ .

$x = (x + \frac{- 1 \cdot 8}{8} + \frac{3}{8}) \cdot 4$

Step 2.2.1.3

Combine the numerators over the common denominator.

$x = (x + \frac{- 1 \cdot 8 + 3}{8}) \cdot 4$

Step 2.2.1.4

Simplify the numerator.

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Step 2.2.1.4.1

Multiply $- 1$ by $8$ .

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

Step 2.2.1.4.2

Add $- 8$ and $3$ .

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

Step 2.2.1.5

Simplify terms.

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Step 2.2.1.5.1

Move the negative in front of the fraction.

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

Step 2.2.1.5.2

Apply the distributive property.

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

Step 2.2.1.5.3

Move $4$ to the left of $x$ .

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

Step 2.2.1.5.4

Cancel the common factor of $4$ .

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Step 2.2.1.5.4.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

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

Step 2.2.1.5.4.2

Factor $4$ out of $8$ .

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

Step 2.2.1.5.4.3

Cancel the common factor.

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

Step 2.2.1.5.4.4

Rewrite the expression.

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

Step 2.2.1.6

Move the negative in front of the fraction.

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

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4 x$ from both sides of the equation.

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

Step 3.1.2

Subtract $4 x$ from $x$ .

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

Step 3.2

Divide each term in $- 3 x = - \frac{5}{2}$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 x = - \frac{5}{2}$ by $- 3$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2.3.2

Move the negative in front of the fraction.

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

Step 3.2.3.3

Multiply $- \frac{5}{2} (- \frac{1}{3})$ .

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Step 3.2.3.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2.3.3.2

Multiply $\frac{5}{2}$ by $1$ .

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

Step 3.2.3.3.3

Multiply $\frac{5}{2}$ by $\frac{1}{3}$ .

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

Step 3.2.3.3.4

Multiply $2$ by $3$ .

$x = \frac{5}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{6}$

Decimal Form:

$x = 0.8\overline{3}$