# What is the solution set of |2x + 1| > 5?A. {x|1 < x < –3} B. {x|–1 < x < 3} C. {x|x > 2 or x < –3} D. {x|x < 2 or x > –3}

2
by gerhgrehrttj

2014-08-01T19:51:55+05:30
2014-08-01T20:13:40+05:30

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Solution set is the set of all values of x, which satisfy the given condition.
| 2 x + 1 | > 5
Let  a = | 2 x + 1 |
then  a =  2 x + 1    if  2x+1 is positive or zero
=  - 2x -1    if  2x+1 is negative of zero
Let 2x+1 be 0 or more.
so  2x + 1 > 5       =>   2x > 5 - 1 = 4    =>   2x > 4    =>    x > 2
Let 2x+1 be 0 or less
so - 2 x - 1  > 5    =>  -2 x  > 6      =>  -x  > 3    =>  x <  -3
(as When you multiply by -1, the inequality reverses.)

So we have    x > 2  and x < -3.
Answer is option C

There is also a quicker way:
|2x+1| > 5      =>  this is rewritten as
-5 >  2x+1  > 5    Left side gives, x < -3 & right side gives x >2