Solve the Inequality for t -6<2t-5<3

$- 6 < 2 t - 5 < 3$

Step 1

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

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

$- 6 + 5 < 2 t < 3 + 5$

Add $- 6$ and $5$ .

$- 1 < 2 t < 3 + 5$

Add $3$ and $5$ .

$- 1 < 2 t < 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 1}{2} < \frac{2 t}{2} < \frac{8}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{2} < \frac{2 t}{2} < \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{1}{2} < \frac{2 t}{2} < \frac{8}{2}$

Divide $t$ by $1$ .

$- \frac{1}{2} < t < \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

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

Step 6

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{1}{2}, 4)$

Step 7