Question

solve and graph the inequality ( b - 6 < -15 )
a) ( b > -21 )
(number line graph)

b) ( b < -9 )
(number line graph)

c) ( b < \frac{3}{2} )
(number line graph)

d) ( b > \frac{5}{2} )
(number line graph)

Explanation:

Step1: Solve the inequality

To solve \( b - 6 < -15 \), add 6 to both sides of the inequality.
\( b - 6 + 6 < -15 + 6 \)
Simplifying both sides, we get \( b < -9 \).

Step2: Match with the graph

Now we look at the options. Option B has the inequality \( b < -9 \) and the number line should show an open circle at -9 (since the inequality is strict, \( < \), not \( \leq \)) and the arrow pointing to the left (for values less than -9).

Answer:

B. \( b < -9 \) (with the corresponding graph for \( b < -9 \))