Question

4x + 11 < -21
choose 1 answer:
a
<---|---|---|---|---|---o---|---|---|---|---|---|---|---|--->
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
b
<---|---|---|---|---|---•---|---|---|---|---|---|---|---|--->
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
c
<---|---|---|---|---|---o---|---|---|---|---|---|---|---|--->
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
(note: the number line in option c has a pink arrow pointing left from the open circle at -8.)
bonus question

Explanation:

Step1: Solve the inequality \(4x + 11 < -21\)

Subtract 11 from both sides: \(4x + 11 - 11 < -21 - 11\)
Simplify: \(4x < -32\)

Step2: Divide both sides by 4

\(\frac{4x}{4} < \frac{-32}{4}\)
Simplify: \(x < -8\)

Step3: Analyze the number line

The solution \(x < -8\) means an open circle at -8 (since -8 is not included) and the line shaded to the left (for values less than -8). Option C has an open circle at -8 and shading to the left, which matches.

Answer:

C. The number line with an open circle at -8 and shading to the left (from the options provided, the one labeled C with the pink arrow pointing left from an open circle at -8)