Question

which graph represents the solution set of this inequality?
4x + 11 < -21
choose 1 answer:
a
<---|-12-11-10-9-8-7-6-5-4-3-2-1 0 1 2 3--->
(open circle at -8)
b
<---|-12-11-10-9-8-7-6-5-4-3-2-1 0 1 2 3--->
(filled circle at -8)

Explanation:

Step1: Solve the inequality

Start with the inequality \(4x + 11 < -21\). Subtract 11 from both sides: \(4x + 11 - 11 < -21 - 11\), which simplifies to \(4x < -32\). Then divide both sides by 4: \(\frac{4x}{4} < \frac{-32}{4}\), so \(x < -8\).

Step2: Analyze the graph features

The solution \(x < -8\) means we have an open circle at \(-8\) (since the inequality is strict, \(x
eq -8\)) and the arrow points to the left (for values less than \(-8\)). Looking at the options, option A has an open circle at \(-8\) and the arrow to the left, while option B has a closed circle (which would be for \(x\leq -8\), incorrect here).

Answer:

A. The graph with an open circle at -8 and the arrow pointing to the left (the graph labeled A)