Question

-3b - 15 > -24
choose 1 answer:
a
<--(with a blue line from -5 to an open circle at 3)-->
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
b
<--(with a green line from -3 (closed circle) to 10)-->
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
c
<--(with a pink line from -5 to a closed circle at 3)-->
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
6 of 7

Explanation:

Step1: Solve the inequality for \( b \)

Start with the inequality \(-3b - 15 > -24\). First, add 15 to both sides:
\(-3b - 15 + 15 > -24 + 15\)
Simplify: \(-3b > -9\)

Step2: Divide by -3 (reverse inequality)

Divide both sides by -3. Remember, when dividing by a negative number, the inequality sign flips:
\(\frac{-3b}{-3} < \frac{-9}{-3}\)
Simplify: \(b < 3\)

Step3: Analyze the number line

The solution \(b < 3\) means all values less than 3. On a number line, this is an open circle at 3 (since 3 is not included) and an arrow pointing to the left (towards smaller numbers). Option A has an open circle at 3 and the arrow to the left, which matches \(b < 3\). Option B has a closed circle at -3 and arrow right, Option C has a closed circle at 3 and arrow left (which would be \(b \leq 3\), not \(b < 3\)).

Answer:

A. The number line with an open circle at 3 and arrow to the left (representing \( b < 3 \))