Algebra Examples

$- 15 < 3 (x - 5) \leq 2$

Apply the distributive property.

$- 15 < 3 x + 3 \cdot - 5 \leq 2$

Multiply $3$ by $- 5$ .

$- 15 < 3 x - 15 \leq 2$

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

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Add $15$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 15 + 15 < 3 x \leq 2 + 15$

Add $- 15$ and $15$ .

$0 < 3 x \leq 2 + 15$

Add $2$ and $15$ .

$0 < 3 x \leq 17$

Divide each term in the inequality by $3$ .

$\frac{0}{3} < \frac{3 x}{3} \leq \frac{17}{3}$

Divide $0$ by $3$ .

$0 < \frac{3 x}{3} \leq \frac{17}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$0 < \frac{3 x}{3} \leq \frac{17}{3}$

Divide $x$ by $1$ .

$0 < x \leq \frac{17}{3}$

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{17}{3}$

Interval Notation:

$(0, \frac{17}{3}]$