Pre-Algebra Examples

$\frac{5}{2} x - 1 = x + \frac{1}{4}$

Step 1

Combine $\frac{5}{2}$ and $x$ .

$\frac{5 x}{2} - 1 = x + \frac{1}{4}$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{5 x}{2} - 1 - x = \frac{1}{4}$

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $5 x - x \cdot 2$ .

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Step 2.5.1.1.1

Factor $x$ out of $5 x$ .

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

Step 2.5.1.1.2

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

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

Step 2.5.1.1.3

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 2)$ .

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

Step 2.5.1.2

Multiply $- 1$ by $2$ .

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

Step 2.5.1.3

Subtract $2$ from $5$ .

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

Step 2.5.2

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

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

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

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

Step 3.2

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

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Add $1$ and $4$ .

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

Step 4

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

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

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

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{5}{4}$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot \frac{5}{4}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{5}{4}$

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{2}{3} \cdot \frac{5}{4}$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Factor $2$ out of $4$ .

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

Step 5.2.1.1.2

Cancel the common factor.

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

Step 5.2.1.1.3

Rewrite the expression.

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

Step 5.2.1.2

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

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

Step 5.2.1.3

Multiply $3$ by $2$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.8\overline{3}$