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sssssssssssssssssssssssssssssssolve:|2x-3|+|2x+3|=6

sssssssssssssssssssssssssssssssolve:|2x-3|+|2x+3|=6

Grade:12

2 Answers

Vijay
16 Points
7 years ago
the critical points in the given equation are -3/2 and 3/2.
case 1:x
-(2x-3)-(2x+3)=6
-4x=6
x=-3/2
 
case 2: -3
2x-3-(2x+3)=6
6=6
hence,no solution from this case
 
case 3 : x>3/2
2x-3+2x+3=6
4x=6
x=3/2
 
hence x=-3/2 and 3/2
mycroft holmes
272 Points
7 years ago
We have triangle inequality,|a+b| \le |a|+|b| with equality when a, b are of same sign
|3-2x| + |3+2x| \ge 6, based on the above with equality when 2x lies between -3 and 3 i.e. when -\frac{3}{2} \le x \le \frac{3}{2}

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