12.2.2 Linear Inequalities, PT3 Focus Practice


Question 6:
List all the integer values of x which satisfy the following linear inequalities:
–2 < 3x + 1 ≤ 10

Solution:
–2 < 3x + 1
–3 < 3x
x > –1
x = 0, 1, 2, 3, …

3x + 1 ≤ 10
3x ≤ 9
x ≤ 3
x = 3, 2, 1, 0, …

Therefore x = 0, 1, 2, 3


Question 7:
List all the integer values of x which satisfy the following linear inequalities:
–5 < 2x – 3 ≤ 1

Solution:
–5 < 2x – 3
–5 + 3 < 2x
2x > –2
x > –1
x = 0, 1, 2, 3, …  

2x – 3 ≤ 1
2x ≤ 4
x ≤ 2
x = 2, 1, 0, –1, …

Therefore x = 0, 1, 2


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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