Question

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choose the inequality that represents the following graph.

-5 -4 -3 -2 -1 0 1 2 3 4 5

choose 1 answer:

a ( x < 1 )

b ( x leq 1 )

c ( x > 1 )

d ( x geq 1 )

Explanation:

Step1: Analyze the dot on the number line

The dot at 1 is filled (closed), which means 1 is included in the solution set. So the inequality should have a "greater than or equal to" or "less than or equal to" sign with 1. Options A ($x < 1$) and C ($x > 1$) have open conditions (dot would be open), so we can eliminate them.

Step2: Analyze the direction of the line

The line is shaded to the right of 1, which means we are looking for values greater than or equal to 1. Option B ($x \leq 1$) is shaded to the left, so we eliminate it. Option D ($x \geq 1$) has a closed dot at 1 and is shaded to the right, which matches the graph.

Answer:

D. \( x \geq 1 \)