Chemistry Examples

$1 < 4 x + 5 < 17$

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.

$1 - 5 < 4 x < 17 - 5$

Step 1.2

Subtract $5$ from $1$ .

$- 4 < 4 x < 17 - 5$

Step 1.3

Subtract $5$ from $17$ .

$- 4 < 4 x < 12$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 4}{4} < \frac{4 x}{4} < \frac{12}{4}$

Step 3

Divide $- 4$ by $4$ .

$- 1 < \frac{4 x}{4} < \frac{12}{4}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$- 1 < \frac{4 x}{4} < \frac{12}{4}$

Step 4.2

Divide $x$ by $1$ .

$- 1 < x < \frac{12}{4}$

Step 5

Divide $12$ by $4$ .

$- 1 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 3$

Interval Notation:

$(- 1, 3)$

Step 7