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16 Aug 2022, 01:30
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (02:46) correct
55%
(02:50)
wrong
based on 137
sessions
History
Date
Time
Result
Not Attempted Yet
How many real solutions has the following equation got?
\(\frac{|2x - 3|}{5} - \frac{|x + 1|}{5} = x - 2\)
A. None
B. 1
C. 2
D. 3
E. Infinite
Are You Up For the Challenge: 700 Level Questions
\(\frac{|2x - 3|}{5} - \frac{|x + 1|}{5} = x - 2\)
A. None
B. 1
C. 2
D. 3
E. Infinite
Are You Up For the Challenge: 700 Level Questions
16 Aug 2022, 19:16
Kudos
Bookmarks
Bunuel
Critical points
(I) When x<-1, both 2x-3 and x+1 are negative
\(\frac{|2x - 3|}{5} - \frac{|x + 1|}{5} = x - 2\)
\(\frac{3-2x }{5} - \frac{-(x + 1)}{5} = x - 2\)
\(3-2x+x+1=5x-10……..6x=14……x=14/6\)….Not a valid solution as x was taken to be less than -1.
(II) When \(-1\leq x \leq \frac{3}{2}\), 2x-3 is negative while x+1 is positive.
\(\frac{|2x - 3|}{5} - \frac{|x + 1|}{5} = x - 2\)
\(\frac{3-2x }{5} - \frac{x + 1}{5} = x - 2\)
\(3-2x-x-1=5x-10……..8x=12……x=3/2\)….a valid solution.
(I) When x>3/2, both 2x-3 and x+1 are positive.
\(\frac{|2x - 3|}{5} - \frac{|x + 1|}{5} = x - 2\)
\(\frac{2x-3 }{5} - \frac{(x + 1)}{5} = x - 2\)
\(2x-3-x-1=5x-10……..4x=6……x=3/2\)….Not a valid solution as x was taken to be greater than 3/2.
Only ONE valid solution- 3/2
B
