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Updated on: 20 Sep 2018, 07:58
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:05.
Last edited by EgmatQuantExpert on 20 Sep 2018, 07:58, edited 5 times in total.
Last edited by EgmatQuantExpert on 20 Sep 2018, 07:58, edited 5 times in total.
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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:
55%
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Question Stats:
63% (01:45) correct
37%
(01:44)
wrong
based on 1298
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Different methods to solve absolute value equations and inequalities- Exercise Question #2
If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?
Options
Previous Question | Next Question
To read the article: Different methods to solve absolute value equations and inequalities
If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?
Options
- a) 0
b) 1
c) 2
d) 3
e) 4
Previous Question | Next Question
To read the article: Different methods to solve absolute value equations and inequalities
My Approach:
Ix-10I will always be positive and in order for ||x-10|-6|=4 to be true |x-10|=2 or |x-10|=10
1.
x-10=2
x=12
2.
-x+10=2
x=8
--> x=12 or x=8
1.
x-10=20
x=20
2.
-x+10=10
x=0
Please correct me if I am wrong!!
Edited! Was wrong first time...
Ix-10I will always be positive and in order for ||x-10|-6|=4 to be true |x-10|=2 or |x-10|=10
|x-10|=2
1.
x-10=2
x=12
2.
-x+10=2
x=8
--> x=12 or x=8
|x-10|=10
1.
x-10=20
x=20
2.
-x+10=10
x=0
Left with four values: 0,8,10,12
So Answer: E
Please correct me if I am wrong!!
Edited! Was wrong first time...
General Discussion
Updated on: 20 Sep 2018, 21:06
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:10.
Last edited by EgmatQuantExpert on 20 Sep 2018, 21:06, edited 4 times in total.
Last edited by EgmatQuantExpert on 20 Sep 2018, 21:06, edited 4 times in total.
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Solution
Given:
- • We are given that x is an integer, and
• We are also given an absolute value equation, ||x - 10| - 6| = 4
To find:
- • We need to find the number of values of x, that satisfy the given equation
Approach and Working:
- • As seen in the previous question, the first step is to substitute |x - 10| as t, which gives
- o |t - 6| = 4
- o t - 6 = 4, if t ≥ 6
- Implies, t = 10, which is greater than 6
Now, substituting back t as |x - 10|, we get, |x - 10| = 10
This again gives two cases,
Case -1: x – 10 = 10, if x ≥ 10
Implies, x = 20, which is greater than 10
Thus, x = 20, is a possible value of x
Case -2: x – 10 = -10, if x < 10
Implies, x = 0, which is also a possible value
- Implies, t = 2, which is less than 6
Now, substituting back t as |x - 10|, we get, |x - 10| = 2
This again gives two cases,
Case -1: x – 10 = 2, if x ≥ 10
Implies, x = 12, which is greater than 10
Thus, x = 12, is a possible value of x
Case -2: x – 10 = -2, if x < 10
Implies, x = 8, which is less than 10
Thus, x = 8, is also a possible value
• Therefore, the number of possible values of x is 4.
Hence, the correct answer is option E.
Answer: E
