Question 51252This question is from textbook
: 1)solve the inequality 2\x-10\<3 and express the solution as a interval.
2)solve the inequality (x+1)(x-6)<0 and express the solution using interval notation.
This question is from textbook
Answer by THANApHD(104)   (Show Source):
You can put this solution on YOUR website! 2|x-10|<3
so
2(x-10)<3 or -2(x-10)<3
x < 23/2 or x > (-17)/-2
x > 17/2
so interval notation will be (17/2,23/2)
=(8.5,11.5)
2. here either one of the compound must be a negative and other must be positive.
if ( x+1)<0 then (x-6)>0 ---- (1)
or if ( x+1)>0 then (x-6)<0 ---- (2)
cuz to gat a negative as a product of two numbers, the two numbers form should be like P*N or N*P
in first case, x+1<0 and x-6>0
x<-1 and x>6
so the interval notation will be (-**,-1)(6,**)
**- infinity
second case x+1>0 and x-6<0
x>-1 and x<6
so the interval notaion will be (-1,6)
so when we combine these two stuffs we get
(-**,-1)(-1,6)(6,**)
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