Convert to Set Notation 4

$4 < - z - 4 < 11$

Solve $- 8 > z > - 15$ .

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

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

$4 + 4 < - z < 11 + 4$

Add $4$ and $4$ .

$8 < - z < 11 + 4$

Add $11$ and $4$ .

$8 < - z < 15$

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

$8 \cdot - 1 > (- z) \cdot - 1 > 15 \cdot - 1$

Multiply $8$ by $- 1$ .

$- 8 > (- z) \cdot - 1 > 15 \cdot - 1$

Multiply $(- z) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$- 8 > 1 z > 15 \cdot - 1$

Multiply $z$ by $1$ .

$- 8 > z > 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$- 8 > z > - 15$

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

$- 15 < z < - 8$

Use the inequality $- 15 < z < - 8$ to build the set notation.

${z | - 15 < z < - 8}$

Convert to Set Notation 4<-z-4<11

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