7.2.3 Linear Inequalities, PT3 Focus Practice


Question 8:
Given that 3< x2 <4 and x is an integer. List all the possible values of x.

Solution:

3< x2 <4 3 2 <x2< 4 2 9<x2 x>11   or   x2<16 x<18 11<x<18 x=12, 13, 14, 15, 16, 17


Question 9:
Find the biggest and the smallest integer of x that satisfy
3x + 2 ≥ –4 and 4 – x > 0.

Solution:
3x + 2 ≥ –4
3x ≥ –4 – 2
3x ≥ –6
x ≥ –2

4 – x > 0
x > –4
x < 4

Smallest integer of x is –2, and the biggest integer of x is 3.



Question 10:
If xhy satisfy the two inequalities 7 h 2 5 and  3( h+2 )20+h, find the values of x and y.

Solution:

7 h 2 5 h 2 57 h4 h4 3( h+2 )20+h 3h+620+h 2h14 h7 4h7 x=4,y=7

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