Question

1. given the inequality (4x + 2 < -2), (x < -1)\

14b which of the number lines correctly represents the solution set of the inequality?\
(there are four number line options labeled a, b, c, d with different markings on the number lines)

Explanation:

Step1: Solve the inequality \(4x + 2 < -2\)

Subtract 2 from both sides: \(4x + 2 - 2 < -2 - 2\)
Simplify: \(4x < -4\)

Step2: Divide both sides by 4

\(\frac{4x}{4} < \frac{-4}{4}\)
Simplify: \(x < -1\)

Step3: Analyze the number line

The solution \(x < -1\) means an open circle at \(-1\) (since \(x\) is not equal to \(-1\)) and the line shaded to the left (for values less than \(-1\)). Looking at the options, the number line with an open circle at \(-1\) and shading to the left (like option A or the one with open circle at -1 and arrow left) is correct. From the given, the number line with open circle at -1 and shading towards lower numbers (left) matches \(x < -1\).

Answer:

The number line with an open circle at \(-1\) and the line shaded to the left (e.g., the one labeled as the correct representation for \(x < -1\) among the options, likely the first one with open circle at -1 and arrow left).