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04 May 2020, 06:25
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E
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Difficulty:
55%
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Question Stats:
69% (02:18) correct
31%
(02:25)
wrong
based on 571
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If \(|3x - 2 + 4x| > 7\), which of the following is a possible value for x?
A. \(- \frac{2}{3}\)
B. \(- \frac{1}{2}\)
C. \(\frac{3}{4}\)
D. \(\frac{5}{4}\)
E. \(\frac{4}{3}\)
A. \(- \frac{2}{3}\)
B. \(- \frac{1}{2}\)
C. \(\frac{3}{4}\)
D. \(\frac{5}{4}\)
E. \(\frac{4}{3}\)
04 May 2020, 06:43
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Bunuel
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
Given: \(|3x - 2 + 4x| > 7\)
Apply Rule #2 to get: EITHER \(3x - 2 + 4x > 7\) OR \(3x - 2 + 4x < -7\)
Let's deal with each one separately:
Take: \(3x - 2 + 4x > 7\)
Simplify: \(7x - 2 > 7\)
Add 2 to both sides: \(7x > 9\)
Divide both sides by \(7\) to get: \(x > \frac{9}{7}\)
Take: \(3x - 2 + 4x < -7\)
Simplify: \(7x - 2 < -7\)
Add 2 to both sides: \(7x < -5\)
Divide both sides by \(7\) to get: \(x < -\frac{5}{7}\)
So, EITHER \(x > \frac{9}{7}\) OR \(x > -\frac{5}{7}\)
Since \(\frac{4}{3} > \frac{9}{7}\), the correct answer is E
Cheers,
Brent
General Discussion
Updated on: 09 Dec 2023, 04:27
Originally posted by BrushMyQuant on 17 Jul 2021, 10:03.
Last edited by BrushMyQuant on 09 Dec 2023, 04:27, edited 4 times in total.
Last edited by BrushMyQuant on 09 Dec 2023, 04:27, edited 4 times in total.
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\(|3x - 2 + 4x| > 7\)
=> |7x - 2| > 7
Theory : |X| > A
=> X > A or X < -A
A. \(-\frac{2}{3}\) ~ 0.67 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
B. \(-\frac{1}{2}\) = 0.5 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
C. \(\frac{3}{4}\) = 0.75 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
D. \(\frac{5}{4}\) = 1.25 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
E. \(\frac{4}{3}\) = 1.3 > 1.28 => TRUE
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Absolute Values
=> |7x - 2| > 7
Theory : |X| > A
=> X > A or X < -A
| |7x - 2| > 7 so we will have two cases, 7x - 2 > 7 or 7x - 2 < -7 | |
| -Case 1: 7x - 2 > 7 => 7x > 9 => x > \(\frac{9}{7}\) ~ 1.28 | -Case 2: 7x - 2 < -7 => 7x < -5 => x < \(\frac{-5}{7}\) ~ -0.71 |
A. \(-\frac{2}{3}\) ~ 0.67 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
B. \(-\frac{1}{2}\) = 0.5 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
C. \(\frac{3}{4}\) = 0.75 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
D. \(\frac{5}{4}\) = 1.25 Does not fall in the range x < -0.71 or x > 1.28 => FALSE
E. \(\frac{4}{3}\) = 1.3 > 1.28 => TRUE
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Absolute Values
