Algebra Examples

$- 2 < 1 - 2 x \leq 2$

Step 1

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

Tap for more steps...

Step 1.1

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

$- 2 - 1 < - 2 x \leq 2 - 1$

Step 1.2

Subtract $1$ from $- 2$ .

$- 3 < - 2 x \leq 2 - 1$

Step 1.3

Subtract $1$ from $2$ .

$- 3 < - 2 x \leq 1$

Step 2

Divide each term in the inequality by $- 2$ .

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

Step 3

Dividing two negative values results in a positive value.

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

Step 4

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x$ by $1$ .

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

Step 5

Move the negative in front of the fraction.

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$[- \frac{1}{2}, \frac{3}{2})$

Step 8