Question

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}

Answer 1

$|2x+1|>5\\\\2x+1>5\ \vee\ 2x+1<-5\\\\2x>5-1\ \vee\ 2x<-5-1\\\\2x>4\ \vee\ 2x<-6\\\\x>2\ \vee\ x<-3\\\\Answer:C>\{x|\ x>2\ or\ x<-3\}$

Answer 2

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