Algebra Examples

- 9 < 3 + 2 x < 13

$- 9 < 3 + 2 x < 13$

Step 1

Move all terms not containing

x

$x$ from the center section of the inequality.

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Step 1.1

Subtract

3

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

- 9 - 3 < 2 x < 13 - 3

$- 9 - 3 < 2 x < 13 - 3$

Step 1.2

Subtract

3

$3$ from

- 9

$- 9$ .

- 12 < 2 x < 13 - 3

$- 12 < 2 x < 13 - 3$

Step 1.3

Subtract

3

$3$ from

13

$13$ .

- 12 < 2 x < 10

$- 12 < 2 x < 10$

- 12 < 2 x < 10

$- 12 < 2 x < 10$

Step 2

Divide each term in the inequality by

2

$2$ .

\frac{- 12}{2} < \frac{2 x}{2} < \frac{10}{2}

$\frac{- 12}{2} < \frac{2 x}{2} < \frac{10}{2}$

Step 3

Divide

- 12

$- 12$ by

2

$2$ .

- 6 < \frac{2 x}{2} < \frac{10}{2}

$- 6 < \frac{2 x}{2} < \frac{10}{2}$

Step 4

Cancel the common factor of

2

$2$ .

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Step 4.1

Cancel the common factor.

$- 6 < \frac{2 x}{2} < \frac{10}{2}$

Step 4.2

Divide

$x$ by

$1$ .

$- 6 < x < \frac{10}{2}$

Step 5

Divide

$10$ by

$2$ .

$- 6 < x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x < 5$

Interval Notation:

$(- 6, 5)$

Step 7