Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the equation.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

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

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Step 1.5.1.1.1

Factor $x$ out of $5 x$ .

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

Step 1.5.1.1.2

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

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

Step 1.5.1.1.3

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

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

Step 1.5.1.2

Multiply $- 1$ by $4$ .

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

Step 1.5.1.3

Subtract $4$ from $5$ .

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

Step 1.5.2

Multiply $x$ by $1$ .

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

Step 2

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

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Step 2.1

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $1$ from $- 1$ .

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

Step 2.4

Divide $- 2$ by $2$ .

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

Step 3

Multiply both sides of the equation by $4$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

$x = 4 \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $- 1$ .

$x = - 4$