Pre-Algebra Examples

$\frac{2}{3} x - 4 = 1 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

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

$\frac{2 x}{3} - 4 = 1 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{2 x}{3} - 4 = 1 + \frac{1}{4}$

Step 2.1.2

Add $1$ and $\frac{1}{4}$ .

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Step 2.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{2 x}{3} - 4 = \frac{4}{4} + \frac{1}{4}$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{2 x}{3} - 4 = \frac{4 + 1}{4}$

Step 2.1.2.3

Add $4$ and $1$ .

$\frac{2 x}{3} - 4 = \frac{5}{4}$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $4$ to both sides of the equation.

$\frac{2 x}{3} = \frac{5}{4} + 4$

Step 3.2

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

$\frac{2 x}{3} = \frac{5}{4} + 4 \cdot \frac{4}{4}$

Step 3.3

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

$\frac{2 x}{3} = \frac{5}{4} + \frac{4 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 x}{3} = \frac{5 + 4 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $4$ by $4$ .

$\frac{2 x}{3} = \frac{5 + 16}{4}$

Step 3.5.2

Add $5$ and $16$ .

$\frac{2 x}{3} = \frac{21}{4}$

Step 4

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot \frac{21}{4}$

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

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot \frac{21}{4}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot \frac{21}{4}$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot \frac{21}{4}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot \frac{21}{4}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{2} \cdot \frac{21}{4}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{3}{2} \cdot \frac{21}{4}$ .

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Step 5.2.1.1

Multiply $\frac{3}{2}$ by $\frac{21}{4}$ .

$x = \frac{3 \cdot 21}{2 \cdot 4}$

Step 5.2.1.2

Multiply $3$ by $21$ .

$x = \frac{63}{2 \cdot 4}$

Step 5.2.1.3

Multiply $2$ by $4$ .

$x = \frac{63}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{63}{8}$

Decimal Form:

$x = 7.875$

Mixed Number Form:

$x = 7 \frac{7}{8}$