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If x ≠ 2.5 and 2x = |15 - 4x|, then x =
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09 Mar 2021, 07:20
09 Mar 2021, 07:20
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =
[#permalink]
09 Mar 2021, 08:41
09 Mar 2021, 08:41
1
Carcass wrote:
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
Case I:
2x = (15 - 4x)
6x = 15
x = 2.5
Case II:
2x = -(15 - 4x)
2x = -15 + 4x
-2x = -15
x = 7.5
Hence, option E
Retired Moderator
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =
[#permalink]
09 Mar 2021, 12:28
09 Mar 2021, 12:28
Carcass wrote:
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
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
