I had a question about modulus....here is an example
Q.: |x+3| - |4-x|=|8+x| How many solutions does the equation have?
Solution: There are 3 key points here: -8, -3, 4. So we have 4 conditions:
a) x<8--> . We reject the solution because our condition is not satisfied (-1 is not less than -8)
b) -8<=x<-3--> . We reject the solution because our condition is not satisfied (-15 is not within (-8,-3) interval.)
c) -3<=x<4 --> . We reject the solution because our condition is not satisfied (-15 is not within (-3,4) interval.)
d) x>=4 --> . We reject the solution because our condition is not satisfied (-1 is not more than 4)
Is there a reason why in section c) we dont choose -3<=x<=4 and instead just choose -3<=x<4. the same goes for section b) as well
Q.: |x+3| - |4-x|=|8+x| How many solutions does the equation have?
Solution: There are 3 key points here: -8, -3, 4. So we have 4 conditions:
a) x<8--> . We reject the solution because our condition is not satisfied (-1 is not less than -8)
b) -8<=x<-3--> . We reject the solution because our condition is not satisfied (-15 is not within (-8,-3) interval.)
c) -3<=x<4 --> . We reject the solution because our condition is not satisfied (-15 is not within (-3,4) interval.)
d) x>=4 --> . We reject the solution because our condition is not satisfied (-1 is not more than 4)
Is there a reason why in section c) we dont choose -3<=x<=4 and instead just choose -3<=x<4. the same goes for section b) as well
