9

Set 15: Linear Inequalities (Advanced)

Explanation

Answer: A

Solve: 3x+2<53x + 2 < 5 and 3x+2>−53x + 2 > -5

A.

−73<x<1-\frac{7}{3} < x < 1

✓ Correct
B.

−1<x<1-1 < x < 1

C.

x<1x < 1

D.

x>−73x > -\frac{7}{3}

Detailed Explanation

Choice A is correct. Choice A is the correct answer. This is equivalent to ∣3x+2∣<5|3 x+2| < 5. 1. First: 3x<3→x<13x < 3 \rightarrow x < 1 2. Second: 3x>−7→x>−733x > -7 \rightarrow x > -\frac{7}{3} 3. Combine: −73<x<1-\frac{7}{3} < x < 1 Strategic Tip: Solve each independently and find the overlap. Choice B is incorrect because it assumes the lower bound is -1. Choice C is incorrect because it misses the lower bound. Choice D is incorrect because it misses the upper bound.

Key Steps:

•

The correct answer is −73<x<1-\frac{7}{3} < x < 1

Why others are wrong:
B: Choice B 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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