Let's analyze the image you've provided.
Image Description:
- There is a
number line from -5 to 5.
- A
solid dot (closed circle) is placed at
-3, indicating that -3 is
included in the solution.
- A
ray extends to the
right from -3, going through -2, -1, 0, 1, 2, 3, 4, 5, and beyond.
- This represents all values of $ x $ that are
greater than or equal to -3.
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Now, let’s examine the answer choices:
A. $ -3 < x < 5 $
→ This means $ x $ is greater than -3
but less than 5.
But the number line includes
-3 and goes
beyond 5, so this is
incorrect.
B. $ x > -3 $
→ This means $ x $ is greater than -3, but
does not include -3.
However, the number line has a
solid dot at -3, meaning -3
is included. So this is
incorrect.
C. $ -3 \leq x \leq -5 $
→ This says $ x $ is between -3 and -5, inclusive. But -3 is greater than -5, so this interval is
backwards and doesn't make sense. Also, the ray goes to the right, not left. So this is
incorrect.
D. $ x \geq -3 $
→ This means $ x $ is
greater than or equal to -3, which matches:
- The solid dot at -3 (includes -3)
- The arrow going to the right (all numbers greater than -3)
✔ This matches the graph perfectly.
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✔ Final Answer: D. $ x \geq -3 $
Parent Tip: Review the logic above to help your child master the concept of inequalities on a number line.
