Question

which inequalities have the solution set graphed on the number line? select two options.
(number line graph: arrow to the left with an open circle at -4, marking numbers -6, -5, -4, -3, -2, -1, 0, 1, 2)
options:
□ ( x < -4 )
□ ( -4 < x )
□ ( -4 leq x )
□ ( -4 > x )
□ ( x > -4 )

Explanation:

Step1: Analyze the number line graph

The number line has an open circle at -4 and the arrow points to the left, indicating all numbers less than -4. So the solution set is \( x < -4 \), which is equivalent to \( -4 > x \) (since if \( x < -4 \), then -4 is greater than x).

Step2: Evaluate each option

• \( x < -4 \): Matches the solution set (open circle, left arrow).
• \( -4 < x \): This would be numbers greater than -4, opposite of the graph.
• \( -4 \leq x \): Includes -4 and numbers greater, doesn't match.
• \( -4 > x \): Equivalent to \( x < -4 \), matches.
• \( x > -4 \): Numbers greater than -4, opposite of the graph.

Answer:

A. \( x < -4 \), D. \( -4 > x \)