Linear Inequalities Questions and Answers - Form 2 Topical Mathematics

Questions

1. Find without using a calculator, the value of:
   
   
2. Solve and write down all the integral values satisfying the inequality.
   X – 9 ≤ - 4 < 3x – 4
3. Solve the inequality and show the solution on the number line.
   3 – 2x <x <2x + 5
4. Show on a number line the range of all integral values of x which satisfy the following pair of inequalities
   3 – x  ≤ 1 – ½ x
   -½ (x-5) ≤ 7-x
5. Solve the inequalities 4x – 3 ≤6x – 1 <3x + 8; hence represent your solution on a number line
6. Find all the integral values of x which satisfy the inequalities
   2(2-x)< 4x -9 < x + 11
7. Find the inequalities that define the unshaded region
   
   
8. Given that x + y = 8 and x²+ y²=34
   Find the value of:-
   1. x²+2xy+y²
   2. 2xy
9. Find the inequalities satisfied by the region labelled R
   
   
10. The region R is defined by x ≥0, y ≥-2, 2y + x ≤2. By drawing suitable straight line on a sketch, show and label the region R
11. Find all the integral values of x which satisfy the inequality
    3(1+ x) < 5x – 11 < x + 45
12. The vertices of the unshaded region in the figure below are O(0, 0) , B(8, 8) and A (8, 0). Write down the inequalities which satisfy the unshaded region
    
    

Answers

1. 12 x 0.25 – 12.4 ÷ 0.4 x 3
   ⅛ of 2.56 + 8.68
   3 – 31 x 3
   0.32 + 8.68
   ^-90/₉
   = -10
2. x - 9 ≤- 4 <3x – 4
   x – 9 ≤- 4
   x ≤5
   3x – 4 >- 4
   3x >0
   x = 0
   0 >x ≤5
   {1, 2, 3, 4, 5} 
3. x > 3 – 2x
   x ≤^{2x + 5}/₃
   3 – 2x < x
   -2x < x – 3
   -3x < - 3
   x < 1
   2x + 5 ≥3x
   -x  ≥  5
   x ≤-5
   -5 ≤x < 1
   
   
4. 3 - x≤ 1 – ½x
   3 – 1 ≤ x – ½x
   2≤ ½ x
   x≥ 4
   -x + 5≤ 14 – 2x
   2x – x ≤ 14 – 5
   x≤ 9
   4≤ X ≤ 9
   
   
5. 4x – 3 ≤6x – 1
   -2x ≤2
   x ≥-1
   6x – 1 <3x + 8
   3x <9
   x <3
   -1 ≤x <3
   
   
6. 2(2-x ) <4x -9
   4 – 2n <4x -9
   4 + 9 <4x + 2n = 13 6x
   =¹³/₆ < n = 21/6 < n
   and 4x – 9 <x + 11
   4n –n < 11 + 9
   3n < 20
   x < ²⁰/₃= < ²/₃
   Integral values 3, 4, 5, 6
7. L₃ : y ≥ 1
   L₁: y + x ≥ - 1
   L₂: y – x
8. 1. x² + 2xy + y² = x² + xy + xy + y²
      = x(x + y) + y(x + y)
      = (x + y) (x + y)
      ∴ (x + y)2 = 8 x 8 = 64
      
   2. x² + 2xy + y² = 64
      (x² + y²) + 2xy = 64
      34 + 2xy = 64
      2xy = 30
9. Equation of L₁
   (3.5, 4) (0, 2)
   y-2 =    2
   x-0    3.5-0
   3.5y – 7 = 2x
   ∴y =⁴/₇x = 2x
   Inequality of
   y ≤⁴/₇x + 2
   Or
   7y ≤ 4x + 14
   Equation of L₂
   (0, 3) (4, 2)
   y - 2 =  3- 2
   x – 4     0 -4
   -4(y-2) = x-4
   -4y + 8 = x -4
   -4y = x -12
   inequality y ≥- ¼ x + 3
   4y ≥–x + 12
   Equation of L₃
   y - 2 =   2
   x – 4   -0.5
   -0.5(y-2) = 2(x-4)
   -5y + 1 = 2x -8
   -5y = 2x - 9
   y = -4x + 18
   in equality y ≤ -4 x+ 18
10. Lines to be drawn x = 0, y = 2
    2y + x = 2
    

    x	0	2
    y	1	0

    
11. 3(1 + x) < 5x – 11
    3 +3 x) < 5x – 11
    -2x < - 14
    x >7
    5x – 11< 45
    5x < 56
    x < 11.2
    Integral values are 8, 9, 10, 11
12. y ≤ x
    x ≤ 8
    y ≤ 0