Algebra Examples

$11 \leq 6 x + 5 < 83$

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

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

$11 - 5 \leq 6 x < 83 - 5$

Subtract $5$ from $11$ .

$6 \leq 6 x < 83 - 5$

Subtract $5$ from $83$ .

$6 \leq 6 x < 78$

Divide each term in the inequality by $6$ .

$\frac{6}{6} \leq \frac{6 x}{6} < \frac{78}{6}$

Divide $6$ by $6$ .

$1 \leq \frac{6 x}{6} < \frac{78}{6}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$1 \leq \frac{6 x}{6} < \frac{78}{6}$

Divide $x$ by $1$ .

$1 \leq x < \frac{78}{6}$

Divide $78$ by $6$ .

$1 \leq x < 13$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 13$

Interval Notation:

$[1, 13)$