Algebra Examples

$- 9 < 1 - 2 x \leq - 2$

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.

$- 9 - 1 < - 2 x \leq - 2 - 1$

Step 1.2

Subtract $1$ from $- 9$ .

$- 10 < - 2 x \leq - 2 - 1$

Step 1.3

Subtract $1$ from $- 2$ .

$- 10 < - 2 x \leq - 3$

Step 2

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

$\frac{- 10}{- 2} > \frac{- 2 x}{- 2} \geq \frac{- 3}{- 2}$

Step 3

Divide $- 10$ by $- 2$ .

$5 > \frac{- 2 x}{- 2} \geq \frac{- 3}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

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Step 4.1

Cancel the common factor.

$5 > \frac{- 2 x}{- 2} \geq \frac{- 3}{- 2}$

Step 4.2

Divide $x$ by $1$ .

$5 > x \geq \frac{- 3}{- 2}$

Step 5

Dividing two negative values results in a positive value.

$5 > x \geq \frac{3}{2}$

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.

$\frac{3}{2} \leq x < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$\frac{3}{2} \leq x < 5$

Interval Notation:

$[\frac{3}{2}, 5)$

Step 8