Algebra Examples

$- 5 < \frac{2 x - 1}{2} < 0$

Step 1

Solve $- \frac{9}{2} < x < \frac{1}{2}$ .

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Step 1.1

Multiply each term in the inequality by $2$ .

$- 5 \cdot 2 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 1.2

Multiply $- 5$ by $2$ .

$- 10 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$- 10 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 1.3.2

Rewrite the expression.

$- 10 < 2 x - 1 < 0 \cdot 2$

Step 1.4

Multiply $0$ by $2$ .

$- 10 < 2 x - 1 < 0$

Step 1.5

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

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Step 1.5.1

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

$- 10 + 1 < 2 x < 0 + 1$

Step 1.5.2

Add $- 10$ and $1$ .

$- 9 < 2 x < 0 + 1$

Step 1.5.3

Add $0$ and $1$ .

$- 9 < 2 x < 1$

Step 1.6

Divide each term in the inequality by $2$ .

$\frac{- 9}{2} < \frac{2 x}{2} < \frac{1}{2}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{9}{2} < \frac{2 x}{2} < \frac{1}{2}$

Step 1.8

Cancel the common factor of $2$ .

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Step 1.8.1

Cancel the common factor.

$- \frac{9}{2} < \frac{2 x}{2} < \frac{1}{2}$

Step 1.8.2

Divide $x$ by $1$ .

$- \frac{9}{2} < x < \frac{1}{2}$

Step 2

Use the inequality $- \frac{9}{2} < x < \frac{1}{2}$ to build the set notation.

${x | - \frac{9}{2} < x < \frac{1}{2}}$

Step 3