Algebra Examples

$\frac{3}{4} > x + 1 > \frac{1}{2}$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

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Step 1.1

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$\frac{3}{4} - 1 > x > \frac{1}{2} - 1$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} - 1 \cdot \frac{4}{4} > x > \frac{1}{2} - 1$

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 - 1 \cdot 4}{4} > x > \frac{1}{2} - 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $4$ .

$\frac{3 - 4}{4} > x > \frac{1}{2} - 1$

Step 1.5.2

Subtract $4$ from $3$ .

$\frac{- 1}{4} > x > \frac{1}{2} - 1$

Step 1.6

Move the negative in front of the fraction.

$- \frac{1}{4} > x > \frac{1}{2} - 1$

Step 1.7

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{4} > x > \frac{1}{2} - 1 \cdot \frac{2}{2}$

Step 1.8

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

$- \frac{1}{4} > x > \frac{1}{2} + \frac{- 1 \cdot 2}{2}$

Step 1.9

Combine the numerators over the common denominator.

$- \frac{1}{4} > x > \frac{1 - 1 \cdot 2}{2}$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Multiply $- 1$ by $2$ .

$- \frac{1}{4} > x > \frac{1 - 2}{2}$

Step 1.10.2

Subtract $2$ from $1$ .

$- \frac{1}{4} > x > \frac{- 1}{2}$

Step 1.11

Move the negative in front of the fraction.

$- \frac{1}{4} > x > - \frac{1}{2}$

Step 2

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{1}{2}, - \frac{1}{4})$

Step 4