7.2.2 Linear Inequalities, PT3 Focus Practice

                 
         
Question 5:
          
Solve each of the following inequalities.
          
(a) 3x + 4 > 5x – 10
          
(b)   –3  ≤ 2x + 1 < 7
          

         
          
Solution:
          
(a)
          
3x + 4 > 5x – 10
          
3x – 5x > –10 – 4
          
–2x > –14
          
x > –7
          
x < 7
       
          
          

          (b)
          
–3 ≤ 2x + 1 < 7
          
–3 ≤ 2x + 1   and   2x + 1 < 7
          
–2x  ≤ 1 + 3   and   2x < 7 – 1
          
–2x  ≤ 4 and   2x < 6
          
≥ –2   and   x < 3
  
                 
The solution is –2 ≤ x < 3.
       
       
  

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