Linear inequalities Questions and Answers

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

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

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

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

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

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