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If |x + 1| = 2|x - 1|, what is the sum of the roots?
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10 Mar 2021, 09:42
10 Mar 2021, 09:42
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Question Stats:
75% (01:47) correct
25% (02:18) wrong based on 24 sessions
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If |x + 1| = 2|x - 1|, what is the sum of the roots?
A. 4
B. 6
C. 8
D. 20/3
E. 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 4
B. 6
C. 8
D. 20/3
E. 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: If |x + 1| = 2|x - 1|, what is the sum of the roots?
[#permalink]
10 Mar 2021, 09:48
10 Mar 2021, 09:48
1
By squaring on both the sides, we will get
\((x+1)^2\) = 4 \((x-1)^2\)
\(x^2 + 2x + 1\) = 4 \(( x^2 -2x + 1)\)
\(x^2 + 2x + 1\) = \(4x^2 - 8x + 4\)
\(3x^2 - 10x +3\) = 0
We are asked the sum of roots. Sum of roots for ax^2 + bx + c = 0 is\(\frac{-b}{a}\)
Here it is \(\frac{10}{3}\)
Answer E
\((x+1)^2\) = 4 \((x-1)^2\)
\(x^2 + 2x + 1\) = 4 \(( x^2 -2x + 1)\)
\(x^2 + 2x + 1\) = \(4x^2 - 8x + 4\)
\(3x^2 - 10x +3\) = 0
We are asked the sum of roots. Sum of roots for ax^2 + bx + c = 0 is\(\frac{-b}{a}\)
Here it is \(\frac{10}{3}\)
Answer E
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Re: If |x + 1| = 2|x - 1|, what is the sum of the roots?
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10 Mar 2021, 10:16
10 Mar 2021, 10:16
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Carcass wrote:
If |x + 1| = 2|x - 1|, what is the sum of the roots?
A. 4
B. 6
C. 8
D. 20/3
E. 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 4
B. 6
C. 8
D. 20/3
E. 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
Given: |x+1|=2|x-1|
So, EITHER x+1=2(x-1) OR x+1=-[2(x-1)]
x+1=2(x-1)
Expand: x + 1 = 2x - 2
Solve: x = 3
x+1=-[2(x-1)]
Expand: x + 1 = -2x + 2
Solve: x = 1/3
When we plug the solutions into the original equation, we find that there are no extraneous roots
So, the SUM of the solutions = 3 + 1/3
= 3 1/3
= 10/3
Answer: E
