Algebra Examples

$\frac{1}{4} < x - 2 < \frac{7}{6}$

Step 1

Add $2$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$\frac{1}{4} + 2 < x < \frac{7}{6} + 2$

Step 2

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

$\frac{1}{4} + 2 \cdot \frac{4}{4} < x < \frac{7}{6} + 2$

Step 3

Combine $2$ and $\frac{4}{4}$ .

$\frac{1}{4} + \frac{2 \cdot 4}{4} < x < \frac{7}{6} + 2$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 2 \cdot 4}{4} < x < \frac{7}{6} + 2$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $4$ .

$\frac{1 + 8}{4} < x < \frac{7}{6} + 2$

Step 5.2

Add $1$ and $8$ .

$\frac{9}{4} < x < \frac{7}{6} + 2$

Step 6

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{9}{4} < x < \frac{7}{6} + 2 \cdot \frac{6}{6}$

Step 7

Combine $2$ and $\frac{6}{6}$ .

$\frac{9}{4} < x < \frac{7}{6} + \frac{2 \cdot 6}{6}$

Step 8

Combine the numerators over the common denominator.

$\frac{9}{4} < x < \frac{7 + 2 \cdot 6}{6}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $2$ by $6$ .

$\frac{9}{4} < x < \frac{7 + 12}{6}$

Step 9.2

Add $7$ and $12$ .

$\frac{9}{4} < x < \frac{19}{6}$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$\frac{9}{4} < x < \frac{19}{6}$

Interval Notation:

$(\frac{9}{4}, \frac{19}{6})$

Step 11