Question

choose 1 answer:
a ( x < -4 )
b ( x leq -4 )
c ( x > -4 )
d ( x geq -4 )

Explanation:

Step1: Analyze the number line

The number line has a filled - in dot at - 4, and the arrow is pointing to the right. A filled - in dot on a number line for an inequality means that the point itself is included in the solution set. An arrow pointing to the right indicates that we are including all numbers greater than or equal to the point (since the dot is filled and the direction is right).

Step2: Match with the inequality options

• Option A: \(x < - 4\) would have an open dot at - 4 and an arrow to the left, so it's incorrect.
• Option B: \(x\leq - 4\) would have a filled dot at - 4 but an arrow to the left, so it's incorrect.
• Option C: \(x > - 4\) would have an open dot at - 4 and an arrow to the right, so it's incorrect.
• Option D: \(x\geq - 4\) has a filled dot at - 4 (indicating - 4 is included) and an arrow to the right (indicating all numbers greater than - 4 are included), which matches the number line.

Answer:

D. \(x\geq - 4\)