Solve for t -5<=-4t-7<=9

$- 5 \leq - 4 t - 7 \leq 9$

Step 1

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

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

$- 5 + 7 \leq - 4 t \leq 9 + 7$

Add $- 5$ and $7$ .

$2 \leq - 4 t \leq 9 + 7$

Add $9$ and $7$ .

$2 \leq - 4 t \leq 16$

Step 2

Divide each term in the inequality by $- 4$ .

$\frac{2}{- 4} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Step 3

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{- 4} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$\frac{2 \cdot 1}{2 \cdot - 2} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot - 2} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Rewrite the expression.

$\frac{1}{- 2} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{2} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Step 5

Cancel the common factor of $- 4$ .

Cancel the common factor.

$- \frac{1}{2} \geq \frac{- 4 t}{- 4} \geq \frac{16}{- 4}$

Divide $t$ by $1$ .

$- \frac{1}{2} \geq t \geq \frac{16}{- 4}$

Step 6

Divide $16$ by $- 4$ .

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

Step 7

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

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

Step 8

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$[- 4, - \frac{1}{2}]$

Step 9