12.2 Linear Inequalities, PT3 Focus Practice


12.2 Linear Inequalities, PT3 Focus Practice
Question 1:
Draw a number line to represent the solution for the linear inequalities –3 < 5 – x ≤ 4.
 
Solution:
–3 < 5 – x and   5 – x ≤ 4
x < 5 + 3   and   x ≤ 4 – 5
x < 8 and   x ≤ –1 → x ≥ 1

Thus, the solution is 1 ≤ x < 8


Question 2:
Solve the following simultaneous linear inequalities.
3 x 5 1 and 2 1 3 x < 3  

Solution:
3x – 5 ≤ 1
3x ≤ 1 + 5
3x ≤ 6
x ≤ 2
2 1 3 x < 3 6 x < 9 Multiply by 3 x < 9 6 x < 3 x > 3 Multiply by 1  
The solution is –3 < x ≤ 2.


Question 3:
The solution for the inequality 2 + < 3x – 4 is
  
Solution:
2 + x < 3x – 4  
x – 3x < –4 – 2
–2x < –6
x < –3
x > 3


Question 4:
The solution for the inequality –2(6y + 3) < 3(4 – 2y) is


Solution:
–2(6y + 3) < 3(4 – 2y)
–12y – 6 < 12 – 6y
–12y + 6y< 12 + 6
–6y < 18
y < 3
y > –3 


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
x≥ –2   and   x < 3

The solution is –2 ≤ x < 3.

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