Question

this question has two parts. first, answer part a. then, answer part b.
part a
solve the inequality -27 < -3u and write the solution in set - builder notation.
part b
graph the solution on a number line.

Explanation:

Step1: Solve the inequality

Given \(-27 < -3u\).
Divide both sides by \(-3\). When dividing an inequality by a negative number, the direction of the inequality sign changes. So, \(\frac{-27}{-3}>u\), which simplifies to \(9 > u\) or \(u < 9\). In set - builder notation, this is \(\{u|u < 9\}\).

Step2: Analyze the graph

For the inequality \(u < 9\), on a number line, we have an open circle at \(9\) (because \(u\) is not equal to \(9\)) and the arrow points to the left (towards smaller numbers).

Answer:

• Part A: \(\{u|u < 9\}\)
• Part B: The correct graph is the one with an open - circle at \(9\) and an arrow pointing to the left (assuming option B in the given graph choices is the one with open - circle at \(9\) and left - pointing arrow).