5

Set 5: Linear Inequalities (Advanced)

Explanation

Answer: B

Which graph correctly represents the solution to x2x \geq -2?

A.

Open circle at -2, shading to the left

B.

Closed circle at -2, shading to the right

✓ Correct
C.

Open circle at -2, shading to the right

D.

Closed circle at -2, shading to the left

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Graphing inequalities on a number line requires understanding symbols and shading. 1. Symbol interpretation: \geq means "greater than or equal to", so include -2 itself (closed circle) 2. Direction: "Greater than" means values to the right on the number line 3. Result: Closed circle at -2, shading right Strategic Tip: Use closed circles for \leq or \geq (includes the value), open circles for << or >> (excludes the value). Choice A is incorrect because it uses an open circle (excluding -2) and shades left (less than), both wrong. Choice C is incorrect because while it shades right (correct direction), it uses an open circle, excluding -2. Choice D is incorrect because it has a closed circle (correct) but shades left, representing x2x \leq -2 instead.

Key Steps:

The correct answer is Closed circle at -2, shading to the right

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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