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What is the solution range satisfying 1/3(x + 4), if we have

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What is the solution range satisfying 1/3(x + 4), if we have

by Max@Math Revolution » Thu Dec 26, 2019 11:29 pm
[GMAT math practice question]

What is the solution range satisfying 1/3(x + 4), if we have |x - 2| ≤ 3?

A. -3 ≤ 1/3(x + 4) ≤ 3
B. -1 ≤ 1/3(x + 4) ≤ 2
C. -2 ≤ 1/3(x + 4) ≤ 1
D. 1 ≤ 1/3(x + 4) ≤ 3
E. 0 ≤ 1/3(x + 4) ≤ 3
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by Max@Math Revolution » Sun Dec 29, 2019 5:54 pm
=>

|x - 2| ≤ 3
=> -3 ≤ x - 2 ≤ 3
=> -3 + 2 ≤ x ≤ 3 + 2
=> -1 ≤ x ≤ 5
=> -1 + 4 ≤ x + 4 ≤ 5 + 4
=> 3 ≤ x + 4 ≤ 9
=> (1/3)(3) ≤ (1/3)(x + 4) ≤ (1/3)(9)
=> 1 ≤ (1/3)(x + 4) ≤ 3

Therefore, D is the answer.
Answer: D
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by deloitte247 » Thu Jan 02, 2020 6:12 pm
Given that |x - 2| ≤ 3
Hence, -3 ≤ x - 2 ≤ 3
-3+2 ≤ x-2+2 ≤ 3+2
-1 ≤ x ≤ 5 ------ Eqn (1)
For the range of 1/3 (x+4), add 4 to both sides of Eqn (1)
-1+4 ≤ x+4 ≤ 5+4
3 ≤ x+4 ≤ 9
Multiply all sides by 1/3
$$\frac{1}{3}\cdot3\le\frac{1}{3}\left(x+4\right)\le\frac{1}{3}\cdot9$$
$$\frac{3}{3}\le\frac{1}{3}\left(x+4\right)\le\frac{9}{3}$$
$$1\le\frac{1}{3}\left(x+4\right)\le3$$

Therefore, the correct answer is option D.
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