Question

Need help with 14. The answer has to to also be in set builder and standard notation.

Answer 1

- The question would like us to solve the following inequality:

`-4z-2>-22`

- The solution is given below:

`\begin{gathered} -4z-2>-22 \\ Add\text{ 2 to both sides} \\ -4z-2+2>-22+2 \\ -4z>-20 \\ \text{ Divide both sides by -4} \\ -(4z)/(-4)>-(20)/(-4) \\ \\ \text{ By dividing by a negative number, the inequality sign must change to its inverse} \\ \\ z<5 \end{gathered}`

- Thus, we need to put the solution in both Set-builder notation and Interval notation. This is done below:

Set-builder notation:

`\begin{gathered} z<5 \\ \lbrace z\in\mathbf{R}|z<5\rbrace \end{gathered}`

Interval notation:

`\begin{gathered} z<5 \\ (-\infty,5) \end{gathered}`