Pre-Algebra Examples

$- 15 < 3 (t - 2) < 24$

Step 1

Apply the distributive property.

$- 15 < 3 t + 3 \cdot - 2 < 24$

Step 2

Multiply $3$ by $- 2$ .

$- 15 < 3 t - 6 < 24$

Step 3

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

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Step 3.1

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 15 + 6 < 3 t < 24 + 6$

Step 3.2

Add $- 15$ and $6$ .

$- 9 < 3 t < 24 + 6$

Step 3.3

Add $24$ and $6$ .

$- 9 < 3 t < 30$

Step 4

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} < \frac{3 t}{3} < \frac{30}{3}$

Step 5

Divide $- 9$ by $3$ .

$- 3 < \frac{3 t}{3} < \frac{30}{3}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

$- 3 < \frac{3 t}{3} < \frac{30}{3}$

Step 6.2

Divide $t$ by $1$ .

$- 3 < t < \frac{30}{3}$

Step 7

Divide $30$ by $3$ .

$- 3 < t < 10$

Step 8