Algebra Examples

$2 < \frac{x}{3} + 8 < 17$

Step 1

Subtract $8$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$2 - 8 < \frac{x}{3} < 17 - 8$

Step 2

Subtract $8$ from $2$ .

$- 6 < \frac{x}{3} < 17 - 8$

Step 3

Multiply each term in the inequality by $3$ .

$- 6 \cdot 3 < \frac{x}{3} \cdot 3 < 17 \cdot 3 - 8 \cdot 3$

Step 4

Multiply $- 6$ by $3$ .

$- 18 < \frac{x}{3} \cdot 3 < 17 \cdot 3 - 8 \cdot 3$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$- 18 < \frac{x}{3} \cdot 3 < 17 \cdot 3 - 8 \cdot 3$

Step 5.2

Rewrite the expression.

$- 18 < x < 17 \cdot 3 - 8 \cdot 3$

Step 6

Simplify each term.

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Step 6.1

Multiply $17$ by $3$ .

$- 18 < x < 51 - 8 \cdot 3$

Step 6.2

Multiply $- 8$ by $3$ .

$- 18 < x < 51 - 24$

Step 7

Subtract $24$ from $51$ .

$- 18 < x < 27$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- 18 < x < 27$

Interval Notation:

$(- 18, 27)$

Step 9