Algebra Examples

$5 < 2 x + 3 < 17$

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.

$5 - 3 < 2 x < 17 - 3$

Step 1.2

Subtract $3$ from $5$ .

$2 < 2 x < 17 - 3$

Step 1.3

Subtract $3$ from $17$ .

$2 < 2 x < 14$

Step 2

Divide each term in the inequality by $2$ .

$\frac{2}{2} < \frac{2 x}{2} < \frac{14}{2}$

Step 3

Divide $2$ by $2$ .

$1 < \frac{2 x}{2} < \frac{14}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$1 < \frac{2 x}{2} < \frac{14}{2}$

Step 4.2

Divide $x$ by $1$ .

$1 < x < \frac{14}{2}$

Step 5

Divide $14$ by $2$ .

$1 < x < 7$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 7$

Interval Notation:

$(1, 7)$

Step 7