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22 Oct 2018, 01:26
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
94% (01:09) correct
6%
(01:50)
wrong
based on 749
sessions
History
Date
Time
Result
Not Attempted Yet
If x ≠ 2.5 and 2x = |15 - 4x|, then x =
A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5
A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5
05 Aug 2020, 10:10
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Bunuel
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
Given: |15 - 4x| = 2x
So, EITHER 15 - 4x = 2x OR 15 - 4x = -2x
Let's test each case.
Take: 15 - 4x = 2x
Add 4x to both sides: 15 = 6x
Solve: x = 15/6 = 5/2 = 2.5
Since we're told x ≠ 2.5, we can stop pursuing this case
Take: 15 - 4x = -2x
Add 4x to both sides: 15 = 2x
Solve: x = 15/2 = 7.5
NOTE: Since we've already seen that x = 2.5 is NOT a solution, we can be certain (without testing) that the correct answer must be x = 7.5
Answer: E
Cheers,
Brent
General Discussion
22 Oct 2018, 01:34
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Bunuel
Given, |15 - 4x|= 2x
Or, -(15-4x)=2x; ( |15-4x|=-(15-4x) when (15-4x)<0 or, 15<4x or,x>3.75 )
Or, 4x-15=2x
Or, 2x=15
Or, x=7.5
Ans. (E)
22 Oct 2018, 04:57
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2x= |15-4x| means 2x= 15-4x; 2x+6x= 15; 8x= 15; x= \(\frac{15}{6}\)= 2.5 (Not Possible given)
OR
2x= |15-4x| means 2x= -(15-4x); 2x= -15+4x; 2x= 15; x= \(\frac{15}{7}\)= 7.5
Answer: E
OR
2x= |15-4x| means 2x= -(15-4x); 2x= -15+4x; 2x= 15; x= \(\frac{15}{7}\)= 7.5
Answer: E
