Question

which number line shows the solution to: 11x + 14 < -8?

Explanation:

Step1: Solve the inequality for x

Subtract 14 from both sides of the inequality \(11x + 14 < -8\):
\(11x + 14 - 14 < -8 - 14\)
\(11x < -22\)

Step2: Divide both sides by 11

Divide each side by 11 to isolate x:
\(\frac{11x}{11} < \frac{-22}{11}\)
\(x < -2\)

Step3: Analyze the number line

The solution \(x < -2\) means we have an open circle at -2 (since the inequality is strict, not "less than or equal to") and the line is shaded to the left of -2 (because x is less than -2). Looking at the options, we need to find the number line with an open circle at -2 and shading to the left. From the given number lines (A, B, C, D), we check the position of the open circle and the direction of the shading. The number line that matches \(x < -2\) will have the open circle at -2 and the arrow pointing left (towards more negative numbers).

Answer:

Assuming the number lines are labeled with D having the open circle at -2 and shading to the left (based on the inequality solution \(x < -2\)), the answer is D. (Note: The exact visual of the number lines is as per the problem's image, but the solution to the inequality \(x < -2\) corresponds to a number line with open circle at -2 and left - ward shading, which should match option D as per typical number line representations for this inequality.)