Solution
- The question would like us to solve the following inequality:
[tex]-4z-2>-22[/tex]
- The solution is given below:
[tex]\begin{gathered} -4z-2>-22 \\ Add\text{ 2 to both sides} \\ -4z-2+2>-22+2 \\ -4z>-20 \\ \text{ Divide both sides by -4} \\ -\frac{4z}{-4}>-\frac{20}{-4} \\ \\ \text{ By dividing by a negative number, the inequality sign must change to its inverse} \\ \\ z<5 \end{gathered}[/tex]
- Thus, we need to put the solution in both Set-builder notation and Interval notation. This is done below:
Set-builder notation:
[tex]\begin{gathered} z<5 \\ \lbrace z\in\mathbf{R}|z<5\rbrace \end{gathered}[/tex]
Interval notation:
[tex]\begin{gathered} z<5 \\ (-\infty,5) \end{gathered}[/tex]
