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Can anyone please explain this question ?

Posted from my mobile device

Let x+4 = y —> x = y - 4
Given, |x - 2| ≤ 3
—> |y - 4 - 2| ≤ 3
—> |y - 6| ≤ 3

Formula: If |x| ≤ a, then -a ≤ x ≤ a
—> -3 ≤ y - 6 ≤ 3
Add 6 to all the sides,
—> -3 + 6 ≤ y - 6 + 6 ≤ 3 + 6
—> 3 ≤ y ≤ 9
Divide by 3 to all the sides
—> 3/3 ≤ y/3 ≤ 9/3
—> 1 ≤ 1/3(x + 4) ≤ 3

Option D
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Hey there look the solution to this would be x-2<=3
And x-2>=-3 now sloving them you get the range of the inequality that is x<=5 and x>=-1

Now simplyfy the inequalities in the answer and check which one gives the following solutions in the answer tab and then finally see that option which simplifies as explained since the option d simplies in similar way option d will be the answer since no other will satisfy the equation range 13(x+4)
Hope this is correct and answer your doubt please let me know i am incorrect.
Cheers!

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=>


\(|x - 2| ≤ 3\)

=> \(-3 ≤ x - 2 ≤ 3\)

=> \(-3 + 2 ≤ x ≤ 3 + 2\)

=> \(-1 ≤ x ≤ 5\)

=> \(-1 + 4 ≤ x + 4 ≤ 5 + 4\)

=> \(3 ≤ x + 4 ≤ 9\)

=> \(\frac{3}{3} ≤ (\frac{1}{3})(x + 4) ≤ \frac{9}{3}\)

=> \(1 ≤ (\frac{1}{3})(x + 4) ≤ 3\)

Therefore, D is the answer.
Answer: D
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[GMAT math practice question]

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

A. \(-3 ≤ \frac{1}{3}(x + 4) ≤ 3 \)

B. \(-1 ≤ \frac{1}{3}(x + 4) ≤ 2\)

C. \(-2 ≤ \frac{1}{3}(x + 4) ≤ 1\)

D. \(1 ≤ \frac{1}{3}(x + 4) ≤ 3 \)

E. \(0 ≤ \frac{1}{3}(x + 4) ≤ 3\)
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MathRevolution
[GMAT math practice question]

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

A. \(-3 ≤ \frac{1}{3}(x + 4) ≤ 3 \)

B. \(-1 ≤ \frac{1}{3}(x + 4) ≤ 2\)

C. \(-2 ≤ \frac{1}{3}(x + 4) ≤ 1\)

D. \(1 ≤ \frac{1}{3}(x + 4) ≤ 3 \)

E. \(0 ≤ \frac{1}{3}(x + 4) ≤ 3\)


ALready discussed
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=>

\(|x - 2| ≤ 3\)

\(=> -3 ≤ x – 2 ≤ 3\)

\(=> -3 + 2 ≤ x ≤ 3 + 2\)

\(=> -1 ≤ x ≤ 5\)

\(=> -1 + 4 ≤ x + 4 ≤ 5 + 4\)

\(=> 3 ≤ x + 4 ≤ 9\)

\(=> (\frac{1}{3})(3) ≤ (\frac{1}{3})(x + 4) ≤ (\frac{1}{3})(9)\)

\(=> 1 ≤ (\frac{1}{3})(x + 4) ≤ 3\)

Therefore, D is the answer.
Answer: D
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