Algebra Examples

$- 5 < 5 + 2 x < 11$

Step 1

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

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Step 1.1

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 5 < 2 x < 11 - 5$

Step 1.2

Subtract $5$ from $- 5$ .

$- 10 < 2 x < 11 - 5$

Step 1.3

Subtract $5$ from $11$ .

$- 10 < 2 x < 6$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 10$ by $2$ .

$- 5 < \frac{2 x}{2} < \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$- 5 < \frac{2 x}{2} < \frac{6}{2}$

Step 4.2

Divide $x$ by $1$ .

$- 5 < x < \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- 5 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 3$

Interval Notation:

$(- 5, 3)$

Step 7