SOLUTION: Hello out there,I really need some help with some problems,the first one is Solve the inequality:[2x]<8.The next one is,Solve the inequality:[p+2]<6.The third is,Solve the inequali

Question 98512: Hello out there,I really need some help with some problems,the first one is Solve the inequality:[2x]<8.The next one is,Solve the inequality:[p+2]<6.The third is,Solve the inequality:Solve the inequality:[z+3]>2.And the last one is,Which of the points satisfy y-3<2x? (0,0)or(1,5)or(-2,0).Thanks for anyone that can help.
Answer by mathslover(157) (Show Source): You can put this solution on YOUR website!
Before giving out the solution to the problem here is something you should
know
[x] means the greatest integer value less than or equal to x
so for e.g [1.2] = 1
[-5.6] = -6
[4]=4
now to the questions
1. [2x] < 8
2[x] < 8 (Note [2x] is not = 2[x] but [2x] <= 2[x] so without loss of inequality we can write [2x] as 2[x]) in the above inequality
[x]< 4

for all x < 4, [x] <4
hence solution set for the above is x< 4
2. [ p + 2] <6
for all p+2 < 6 , [p+2] will be less than 6
p < 4
3 [z +3 ] >2
since [z+3] is an integer value [z+3] should be >=3 ( integer greater than 2)
which gives z>=0
4.y-3<2x? (0,0)or(1,5)or(-2,0).
substitue x=0, y=0
0-3< 2*0
-3 <0 hence it satisfies the equation
Substituting x=1 , y=5
5-3 < 2*1
2< 2
It does not satisfy the equation
Substituting x= -2 , y=0
0 - 3 < 2* -2
-3 < -4
it does not satisfy the equation
The only point satisfying the equation is (0,0)

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