Algebra Examples

$\frac{1}{4} x - 3 = \frac{1}{2} x + 8$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

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

$\frac{1}{4} x - 3 - \frac{1}{2} x = 8$

Step 1.2

Subtract $8$ from both sides of the equation.

$\frac{1}{4} x - 3 - \frac{1}{2} x - 8 = 0$

Step 2

Simplify $\frac{1}{4} x - 3 - \frac{1}{2} x - 8$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{x}{4} - 3 - \frac{1}{2} x - 8 = 0$

Step 2.1.2

Combine $x$ and $\frac{1}{2}$ .

$\frac{x}{4} - 3 - \frac{x}{2} - 8 = 0$

Step 2.2

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

$\frac{x}{4} - \frac{x}{2} \cdot \frac{2}{2} - 3 - 8 = 0$

Step 2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$\frac{x}{4} - \frac{x \cdot 2}{2 \cdot 2} - 3 - 8 = 0$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{x}{4} - \frac{x \cdot 2}{4} - 3 - 8 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{4} - 3 - 8 = 0$

Step 2.5

Find the common denominator.

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Step 2.5.1

Write $- 3$ as a fraction with denominator $1$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3}{1} - 8 = 0$

Step 2.5.2

Multiply $\frac{- 3}{1}$ by $\frac{4}{4}$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3}{1} \cdot \frac{4}{4} - 8 = 0$

Step 2.5.3

Multiply $\frac{- 3}{1}$ by $\frac{4}{4}$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3 \cdot 4}{4} - 8 = 0$

Step 2.5.4

Write $- 8$ as a fraction with denominator $1$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3 \cdot 4}{4} + \frac{- 8}{1} = 0$

Step 2.5.5

Multiply $\frac{- 8}{1}$ by $\frac{4}{4}$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3 \cdot 4}{4} + \frac{- 8}{1} \cdot \frac{4}{4} = 0$

Step 2.5.6

Multiply $\frac{- 8}{1}$ by $\frac{4}{4}$ .

$\frac{x - x \cdot 2}{4} + \frac{- 3 \cdot 4}{4} + \frac{- 8 \cdot 4}{4} = 0$

Step 2.6

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2 - 3 \cdot 4 - 8 \cdot 4}{4} = 0$

Step 2.7

Simplify each term.

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Step 2.7.1

Multiply $2$ by $- 1$ .

$\frac{x - 2 x - 3 \cdot 4 - 8 \cdot 4}{4} = 0$

Step 2.7.2

Multiply $- 3$ by $4$ .

$\frac{x - 2 x - 12 - 8 \cdot 4}{4} = 0$

Step 2.7.3

Multiply $- 8$ by $4$ .

$\frac{x - 2 x - 12 - 32}{4} = 0$

Step 2.8

Subtract $2 x$ from $x$ .

$\frac{- x - 12 - 32}{4} = 0$

Step 2.9

Subtract $32$ from $- 12$ .

$\frac{- x - 44}{4} = 0$

Step 2.10

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 44}{4} = 0$

Step 2.11

Rewrite $- 44$ as $- 1 (44)$ .

$\frac{- (x) - 1 (44)}{4} = 0$

Step 2.12

Factor $- 1$ out of $- (x) - 1 (44)$ .

$\frac{- (x + 44)}{4} = 0$

Step 2.13

Rewrite $- (x + 44)$ as $- 1 (x + 44)$ .

$\frac{- 1 (x + 44)}{4} = 0$

Step 2.14

Move the negative in front of the fraction.

$- \frac{x + 44}{4} = 0$