Algebra Examples

$- 9 < 3 + 2 x < 13$

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.

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

Step 1.2

Subtract $3$ from $- 9$ .

$- 12 < 2 x < 13 - 3$

Step 1.3

Subtract $3$ from $13$ .

$- 12 < 2 x < 10$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 12$ by $2$ .

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

Step 4

Cancel the common factor of $2$ .

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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