Algebra Examples

$- 1 \leq 3 - 2 x < 5$

Step 1

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

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Step 1.1

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 - 3 \leq - 2 x < 5 - 3$

Step 1.2

Subtract $3$ from $- 1$ .

$- 4 \leq - 2 x < 5 - 3$

Step 1.3

Subtract $3$ from $5$ .

$- 4 \leq - 2 x < 2$

Step 2

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

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

Step 3

Divide $- 4$ by $- 2$ .

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

Step 4

Cancel the common factor of $- 2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x$ by $1$ .

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

Step 5

Divide $2$ by $- 2$ .

$2 \geq x > - 1$

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.

$- 1 < x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x \leq 2$

Interval Notation:

$(- 1, 2]$

Step 8