Solve for t -4<3t+5<=20

$- 4 < 3 t + 5 \leq 20$

Step 1

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

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

$- 4 - 5 < 3 t \leq 20 - 5$

Subtract $5$ from $- 4$ .

$- 9 < 3 t \leq 20 - 5$

Subtract $5$ from $20$ .

$- 9 < 3 t \leq 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} < \frac{3 t}{3} \leq \frac{15}{3}$

Step 3

Divide $- 9$ by $3$ .

$- 3 < \frac{3 t}{3} \leq \frac{15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 < \frac{3 t}{3} \leq \frac{15}{3}$

Divide $t$ by $1$ .

$- 3 < t \leq \frac{15}{3}$

Step 5

Divide $15$ by $3$ .

$- 3 < t \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < t \leq 5$

Interval Notation:

$(- 3, 5]$

Step 7