Question

this question has two parts. first, answer part a. then, answer part b. part a solve the inequality \\( \frac { 1 } { 5 } z > - 4 \\) and write the solution in set - builder notation. part b graph the solution on a number line. a) b)

Explanation:

Step1: Solve the inequality

Multiply both sides of \(\frac{1}{5}z>-4\) by \(5\) (since \(5>0\), the inequality sign remains the same).
\(\frac{1}{5}z\times5>-4\times5\)
\(z > - 20\)

In set - builder notation, the solution is \(\{z|z > - 20\}\)

Step2: Analyze the number - line graph

For the inequality \(z > - 20\), on the number line, there is an open circle at \(-20\) (because \(z=-20\) is not included in the solution) and the line extends to the right (towards positive infinity).

Answer:

• Part A: The solution in set - builder notation is \(\{z|z > - 20\}\)
• Part B: The correct graph is option A (open circle at \(-20\) and line extending to the right)