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 < -5 )

b ( x leq -5 )

c ( x > -5 )

d ( x geq -5 )

Explanation:

Step1: Analyze the graph's dot

The dot at -5 is open, which means -5 is not included. So we can eliminate options with "≤" or "≥" (B and D).

Step2: Analyze the direction of the line

The line is shaded to the right of -5, which means the values are greater than -5. So the inequality should be \( x > -5 \)? Wait, no, wait. Wait, the arrow: wait, the graph has the open dot at -5 and the line goes to the right? Wait, no, looking at the number line: the open circle is at -5, and the blue line is to the right of -5 (towards positive numbers). Wait, but let's check again. Wait, the number line: -5, -4, -3,... 0, 1,... So the open circle is at -5, and the line is drawn to the right (towards higher numbers). So that means x is greater than -5? But wait, let's check the options. Option C is \( x > -5 \), option A is \( x < -5 \). Wait, maybe I made a mistake. Wait, the arrow: the blue line is going to the right, so from -5 onwards to the right. So open circle means not including -5, and the direction is right (increasing), so x is greater than -5? Wait, but let's re-express. Wait, the open dot at -5: open dot means the inequality is strict (no equal sign). The line is shaded to the right of -5, so x is greater than -5. So the correct option is C? Wait, no, wait the original graph: let me look again. The number line: the open circle is at -5, and the blue line is going to the right (towards positive numbers). So that means all numbers greater than -5 are included. So the inequality is \( x > -5 \), which is option C? Wait, but let's check the options again. Option C is \( x > -5 \), option A is \( x < -5 \), B is \( x \leq -5 \), D is \( x \geq -5 \). So yes, open dot (so no equal sign) and direction right (so greater than), so C. Wait, but maybe I messed up the direction. Wait, the arrow on the number line: the right arrow is towards positive, left towards negative. So if the line is to the right of -5, that's numbers greater than -5. So yes, C.

Answer:

C. \( x > -5 \)