Solve for t 5<2t+7<11

$5 < 2 t + 7 < 11$

Step 1

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$5 - 7 < 2 t < 11 - 7$

Subtract $7$ from $5$ .

$- 2 < 2 t < 11 - 7$

Subtract $7$ from $11$ .

$- 2 < 2 t < 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 2}{2} < \frac{2 t}{2} < \frac{4}{2}$

Step 3

Divide $- 2$ by $2$ .

$- 1 < \frac{2 t}{2} < \frac{4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 < \frac{2 t}{2} < \frac{4}{2}$

Divide $t$ by $1$ .

$- 1 < t < \frac{4}{2}$

Step 5

Divide $4$ by $2$ .

$- 1 < t < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < t < 2$

Interval Notation:

$(- 1, 2)$

Step 7