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Linear inequalities Questions

1.  Find without using a calculator, the value of :

12 0.0625 – 12.4 ÷ 0.4 x 3

1/8 of 2.56 + 8.68  

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  

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7.  Find the inequalities that define the unshaded region

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.  Given that x + y = 8 and x²+ y²=34

 Find the value of:-   a) x²+2xy+y²

 b) 2xy

9.  Find the inequalities satisfied by the region labelled R

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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  

 

Linear inequalities 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

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 – ½ X

3 – 1 ≤ X – ½ X

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

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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.  a)  x2 + 2xy + y2 = x2 + xy + xy + y2

= x(x + y) + y(x + y)

= (x + y) (x + y)

 (x + y)2 = 8 x 8 = 64

 

b)  x2 + 2xy + y2 = 64

   (x2 + y2) + 2xy = 64

34 + 2xy = 64

2xy = 30

Image From EcoleBooks.comImage From EcoleBooks.com9.  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

 

 

10.  Lines to be drawn x = 0, y = 2

  2y + x = 2 x 0 2

 y 1 0

 

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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


 




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