Pre-Algebra Examples

$- \frac{3}{2} < x - \frac{1}{2} < \frac{5}{2}$

Step 1

Add $\frac{1}{2}$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- \frac{3}{2} + \frac{1}{2} < x < \frac{5}{2} + \frac{1}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 3 + 1}{2} < x < \frac{5}{2} + \frac{1}{2}$

Step 3

Simplify the expression.

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Step 3.1

Add $- 3$ and $1$ .

$\frac{- 2}{2} < x < \frac{5}{2} + \frac{1}{2}$

Step 3.2

Divide $- 2$ by $2$ .

$- 1 < x < \frac{5}{2} + \frac{1}{2}$

Step 4

Combine the numerators over the common denominator.

$- 1 < x < \frac{5 + 1}{2}$

Step 5

Simplify the expression.

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Step 5.1

Add $5$ and $1$ .

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

Step 5.2

Divide $6$ by $2$ .

$- 1 < x < 3$

Step 6