Question

this question has two parts. first, answer part a. then, answer part b. part a a. solve the inequality 4b ≤ -3 and write the solution in set-builder notation.

Explanation:

Step1: Isolate the variable \( b \)

To solve the inequality \( 4b \leq -3 \), we divide both sides by 4. Since 4 is a positive number, the direction of the inequality sign remains the same.

$$ \frac{4b}{4} \leq \frac{-3}{4} $$

Simplifying both sides, we get:

$$ b \leq -\frac{3}{4} $$

Step2: Write in set - builder notation

Set - builder notation describes a set by stating the properties that its elements must satisfy. For the solution \( b \leq -\frac{3}{4} \), the set - builder notation is \( \{b\mid b \leq -\frac{3}{4}\} \)

Answer:

\(\{b\mid b \leq -\frac{3}{4}\}\)