Solve for z 0<-z-4<3

$0 < - z - 4 < 3$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$0 + 4 < - z < 3 + 4$

Add $0$ and $4$ .

$4 < - z < 3 + 4$

Add $3$ and $4$ .

$4 < - z < 7$

Step 2

Multiply each term in the inequality by $- 1$ .

$\frac{4}{- 1} > \frac{- z}{- 1} > \frac{7}{- 1}$

Step 3

Divide $4$ by $- 1$ .

$- 4 > \frac{- z}{- 1} > \frac{7}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$- 4 > \frac{z}{1} > \frac{7}{- 1}$

Step 5

Divide $z$ by $1$ .

$- 4 > z > \frac{7}{- 1}$

Step 6

Divide $7$ by $- 1$ .

$- 4 > z > - 7$

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.

$- 7 < z < - 4$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- 7 < z < - 4$

Interval Notation:

$(- 7, - 4)$

Step 9