Algebra Examples

$- \frac{3}{4} x - \frac{1}{3} + \frac{7}{8} x - \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{3}{4}$ .

$- \frac{x \cdot 3}{4} - \frac{1}{3} + \frac{7}{8} x - \frac{1}{2}$

Step 1.2

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

$- \frac{3 \cdot x}{4} - \frac{1}{3} + \frac{7}{8} x - \frac{1}{2}$

Step 1.3

Combine $\frac{7}{8}$ and $x$ .

$- \frac{3 x}{4} - \frac{1}{3} + \frac{7 x}{8} - \frac{1}{2}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3 x}{4}$ by $\frac{6}{6}$ .

$- (\frac{3 x}{4} \cdot \frac{6}{6}) - \frac{1}{3} + \frac{7 x}{8} - \frac{1}{2}$

Step 2.2

Multiply $\frac{3 x}{4}$ by $\frac{6}{6}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{1}{3} + \frac{7 x}{8} - \frac{1}{2}$

Step 2.3

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - (\frac{1}{3} \cdot \frac{8}{8}) + \frac{7 x}{8} - \frac{1}{2}$

Step 2.4

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{8}{3 \cdot 8} + \frac{7 x}{8} - \frac{1}{2}$

Step 2.5

Multiply $\frac{7 x}{8}$ by $\frac{3}{3}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{8}{3 \cdot 8} + \frac{7 x}{8} \cdot \frac{3}{3} - \frac{1}{2}$

Step 2.6

Multiply $\frac{7 x}{8}$ by $\frac{3}{3}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{8}{3 \cdot 8} + \frac{7 x \cdot 3}{8 \cdot 3} - \frac{1}{2}$

Step 2.7

Multiply $\frac{1}{2}$ by $\frac{12}{12}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{8}{3 \cdot 8} + \frac{7 x \cdot 3}{8 \cdot 3} - (\frac{1}{2} \cdot \frac{12}{12})$

Step 2.8

Multiply $\frac{1}{2}$ by $\frac{12}{12}$ .

$- \frac{3 x \cdot 6}{4 \cdot 6} - \frac{8}{3 \cdot 8} + \frac{7 x \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12}$

Step 2.9

Multiply $4$ by $6$ .

$- \frac{3 x \cdot 6}{24} - \frac{8}{3 \cdot 8} + \frac{7 x \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12}$

Step 2.10

Multiply $3$ by $8$ .

$- \frac{3 x \cdot 6}{24} - \frac{8}{24} + \frac{7 x \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12}$

Step 2.11

Reorder the factors of $8 \cdot 3$ .

$- \frac{3 x \cdot 6}{24} - \frac{8}{24} + \frac{7 x \cdot 3}{3 \cdot 8} - \frac{12}{2 \cdot 12}$

Step 2.12

Multiply $3$ by $8$ .

$- \frac{3 x \cdot 6}{24} - \frac{8}{24} + \frac{7 x \cdot 3}{24} - \frac{12}{2 \cdot 12}$

Step 2.13

Multiply $2$ by $12$ .

$- \frac{3 x \cdot 6}{24} - \frac{8}{24} + \frac{7 x \cdot 3}{24} - \frac{12}{24}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 6 - 8 + 7 x \cdot 3 - 12}{24}$

Step 4

Simplify each term.

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Step 4.1

Multiply $6$ by $- 3$ .

$\frac{- 18 x - 8 + 7 x \cdot 3 - 12}{24}$

Step 4.2

Multiply $3$ by $7$ .

$\frac{- 18 x - 8 + 21 x - 12}{24}$

Step 5

Simplify by adding terms.

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Step 5.1

Add $- 18 x$ and $21 x$ .

$\frac{3 x - 8 - 12}{24}$

Step 5.2

Subtract $12$ from $- 8$ .

$\frac{3 x - 20}{24}$