Question

select the correct answer. which number line shows the solution to this compound inequality? 3x - 5 > 1 or -2x ≤ -10

Explanation:

Answer:

First, solve each inequality:

1. For \( 3x - 5>1 \):

• Add 5 to both sides: \( 3x>1 + 5=6 \)
• Divide by 3: \( x > 2 \) (open circle at \( x = 2 \), arrow to the right)

1. For \( - 2x\leq - 10 \):

• Divide both sides by - 2 (and reverse the inequality sign): \( x\geq5 \) (closed circle at \( x = 5 \), arrow to the right)

Since the compound inequality is "or", we take the union of the two solution sets. The solution set is \( x>2 \) (because \( x\geq5 \) is a subset of \( x > 2 \)).

Looking at the options:

• Option A: The red line starts from an open circle at \( x = 2 \) and goes to the right, which matches our solution \( x>2 \).
• Option B: Has two separate segments, which is incorrect as the union of \( x > 2 \) and \( x\geq5 \) is just \( x>2 \).
• Option C: The open circle is at \( x = 5 \), which is incorrect.
• Option D: The red line is in the wrong direction (to the left after some point), which is incorrect.

So the correct answer is A. The number line with an open circle at 2 and a red line extending to the right from 2. So the answer is A.