Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

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

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

Multiply $4$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Find the common denominator.

Tap for more steps...

Step 5.1

Multiply $\frac{- 3 x \cdot 2 + 7 x}{8}$ by $\frac{3}{3}$ .

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

Step 5.2

Multiply $\frac{- 3 x \cdot 2 + 7 x}{8}$ by $\frac{3}{3}$ .

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

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

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

Step 5.6

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

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

Step 5.7

Reorder the factors of $8 \cdot 3$ .

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

Step 5.8

Multiply $3$ by $8$ .

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

Step 5.9

Multiply $3$ by $8$ .

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

Step 5.10

Multiply $2$ by $12$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

Multiply $2$ by $- 3$ .

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

Step 7.2

Add $- 6 x$ and $7 x$ .

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

Step 7.3

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

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

Step 8

Subtract $12$ from $- 8$ .

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