what is the range of x where ||x - 3| - 4| 3?

Question

what is the range of x where ||x - 3| - 4| > 3?
A.( -∞, -4) or (2, 4) or ( 10, ∞)
B.( -∞, -4) or (-2, 4) or ( 10, ∞)
C.( -∞, -4) or ( 10, ∞)
D.( -∞, 4) or ( 10, ∞)
E.( -∞, -4) or (-2, 2) or ( 10, ∞)

nick1816 · Accepted Answer

At x=3,
||x - 3| - 4| > 3
||3-3|-4|>3
4>3 (true)

Eliminate C and E (as the range given in these options doesn't contain 3)

At x=0
||x - 3| - 4| > 3
||0-3|-4|>3
|3-4|>3
1>3 (not true)

Eliminate B and D (as the range given in these options contains 0)

A

nick1816 · Answer

Another way ||x - 3| - 4| > 3 |x - 3| - 4 > 3 or |x - 3| - 4 < -3 Case 1- |x - 3| - 4 > 3 |x - 3| > 7 i). x-3 >7 x >10 .......(1) ii). x-3 < -7 x < -4 ........(2) Case 2- |x - 3| - 4 < -3 |x - 3| < 1 -1 < x - 3 < 1 2 < x < 4 .......(3) From (1), (2) and (3) x∈ ( -∞, -4) or (2, 4) or ( 10, ∞)

Kinshook · Answer

Asked: what is the range of x where ||x - 3| - 4| > 3? ||x - 3| - 4| > 3 Case 1: |x-3|-4 >3 |x-3| >7 x > 10 or x < -4 Case 2: |x-3|-4 <-3 |x-3| < 1 2

gmatophobia · Answer

Assume |x-3| as y, therefore the equation ||x-3|- 4| > 3 translates to

|y - 4| > 3

y > 7 or y < 1

Case 1 : |x-3| > 7 => x > 10 or x < -4

Case 2 : |x-3| < 1 => 2 < x < 4

Combine the ranges in bold-

Option A

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

We need to find the range of x where ||x - 3| - 4| > 3?

|A| > B
=> A > B or A < -B

We have two cases as we have \|\|x - 3\| - 4\| > 3
-Case 1: \|x - 3\| -4 > 3 => \| x - 3 \| > 7 => x - 3 > 7 or x - 3 < -7 => x > 10 or x < -4 => ( -∞, -4) or ( 10, ∞)	-Case 2: \|x - 3\| -4 < -3 => \| x - 3 \| < 1 => -1 < x -3 < 1 => -1 + 3 < x < 1 + 3 => 2 < x < 4 => (2, 4)

So, Answer will be A
Hope it helps!

Watch the following video to MASTER Absolute Values

what is the range of x where ||x - 3| - 4| > 3?

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