Solve the Inequality for z 19>=3z+1>=-5

$19 \geq 3 z + 1 \geq - 5$

Step 1

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$19 - 1 \geq 3 z \geq - 5 - 1$

Subtract $1$ from $19$ .

$18 \geq 3 z \geq - 5 - 1$

Subtract $1$ from $- 5$ .

$18 \geq 3 z \geq - 6$

Step 2

Divide each term in the inequality by $3$ .

$\frac{18}{3} \geq \frac{3 z}{3} \geq \frac{- 6}{3}$

Step 3

Divide $18$ by $3$ .

$6 \geq \frac{3 z}{3} \geq \frac{- 6}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$6 \geq \frac{3 z}{3} \geq \frac{- 6}{3}$

Divide $z$ by $1$ .

$6 \geq z \geq \frac{- 6}{3}$

Step 5

Divide $- 6$ by $3$ .

$6 \geq z \geq - 2$

Step 6

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

$- 2 \leq z \leq 6$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq z \leq 6$

Interval Notation:

$[- 2, 6]$

Step 8