8
algebra

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

A

73<x<1-\frac{7}{3} < x < 1

B

1<x<1-1 < x < 1

C

x<1x < 1

D

x>73x > -\frac{7}{3}

Correct Answer: A

Choice A is the correct answer. This is equivalent to 3x+2<5|3x+2| < 5.

  1. First: 3x<3x<13x < 3 \rightarrow x < 1
  2. Second: 3x>7x>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.