Algebra Examples

$\frac{3}{4} \leq x - \frac{7}{8} < \frac{5}{6}$

Step 1

Add $\frac{7}{8}$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$\frac{3}{4} + \frac{7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 2

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

$\frac{3}{4} \cdot \frac{2}{2} + \frac{7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

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

$\frac{3 \cdot 2}{4 \cdot 2} + \frac{7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{3 \cdot 2}{8} + \frac{7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $3$ by $2$ .

$\frac{6 + 7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 5.2

Add $6$ and $7$ .

$\frac{13}{8} \leq x < \frac{5}{6} + \frac{7}{8}$

Step 6

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{13}{8} \leq x < \frac{5}{6} \cdot \frac{4}{4} + \frac{7}{8}$

Step 7

To write $\frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{13}{8} \leq x < \frac{5}{6} \cdot \frac{4}{4} + \frac{7}{8} \cdot \frac{3}{3}$

Step 8

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 8.1

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{13}{8} \leq x < \frac{5 \cdot 4}{6 \cdot 4} + \frac{7}{8} \cdot \frac{3}{3}$

Step 8.2

Multiply $6$ by $4$ .

$\frac{13}{8} \leq x < \frac{5 \cdot 4}{24} + \frac{7}{8} \cdot \frac{3}{3}$

Step 8.3

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

$\frac{13}{8} \leq x < \frac{5 \cdot 4}{24} + \frac{7 \cdot 3}{8 \cdot 3}$

Step 8.4

Multiply $8$ by $3$ .

$\frac{13}{8} \leq x < \frac{5 \cdot 4}{24} + \frac{7 \cdot 3}{24}$

Step 9

Combine the numerators over the common denominator.

$\frac{13}{8} \leq x < \frac{5 \cdot 4 + 7 \cdot 3}{24}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Multiply $5$ by $4$ .

$\frac{13}{8} \leq x < \frac{20 + 7 \cdot 3}{24}$

Step 10.2

Multiply $7$ by $3$ .

$\frac{13}{8} \leq x < \frac{20 + 21}{24}$

Step 10.3

Add $20$ and $21$ .

$\frac{13}{8} \leq x < \frac{41}{24}$

Step 11

The result can be shown in multiple forms.

Inequality Form:

$\frac{13}{8} \leq x < \frac{41}{24}$

Interval Notation:

$[\frac{13}{8}, \frac{41}{24})$

Step 12