GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
What is the sum of all solutions to the equation
[#permalink]
13 Nov 2016, 09:06
13 Nov 2016, 09:06
1
8
Bookmarks
00:00
Question Stats:
39% (01:54) correct
60% (01:58) wrong based on 92 sessions
Hide Show timer Statistics
What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24?
A) -5
B) -3
C) -2
D) 2
E) 5
A) -5
B) -3
C) -2
D) 2
E) 5
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the sum of all solutions to the equation
[#permalink]
13 Nov 2016, 09:07
13 Nov 2016, 09:07
1
GreenlightTestPrep wrote:
What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24?
A) -5
B) -3
C) -2
D) 2
E) 5
A) -5
B) -3
C) -2
D) 2
E) 5
When solving equations involving ABSOLUTE VALUE, there are 3 steps:
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
So, we have two equations to solve: x² – 4x + 4 = x² + 10x – 24 and x² – 4x + 4 = -(x² + 10x – 24)
x² – 4x + 4 = x² + 10x – 24
Subtract x² from both sides: –4x + 4 = 10x – 24
Rearrange: 28 = 14x
Solve: x = 2
x² – 4x + 4 = -(x² + 10x – 24)
Simplify right side: x² – 4x + 4 = -x² - 10x + 24
Add x² to both sides: 2x² – 4x + 4 = -10x + 24
Add 10x to both sides: 2x² + 6x + 4 = 24
Subtract 24 from both sides: 2x² + 6x - 20 = 0
Factor: 2(x² + 3x - 10) = 0
Factor again: 2(x - 2)(x + 5) = 0
Solve: x = 2 and x = -5
So, we have two solutions to consider: x = 2 and x = -5
Plug solutions into original equation to check for extraneous roots
x = 2
|2² – 4(2) + 4| = 2² + 10(2) – 24
Evaluate: |0| = 0
This works, so keep this solution
x = -5
|(-5)² – 4(-5) + 4| = (-5)² + 10(-5) – 24
Evaluate: |49| = -49
Doesn't work. So, x = -5 is NOT a solution
Since there's only one valid solution (x = 2), the sum of all solutions is 2.
Answer: D
Re: What is the sum of all solutions to the equation
[#permalink]
18 Dec 2016, 08:35
18 Dec 2016, 08:35
This is kind of a bad question because people who neglect the absolute value rule will accidentally get the right answer.
