Module PMR

CHAPTER 5 : LINEAR INEQUALITIES

Identifying relationship greater than (>) and less than (< )

Integers

SMALL BIG

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

DESCRIPTION INEQUALITIES EXAMPLES QUESTIONS(write ‘<’ or ‘>’)

y is greater than xbig small

y > x

big small5 > 2 3 9

6 0-5 -1-2 -24 -47 10-3 -5

big small-1 > -6

y is less than x small big y < x

small big 3 < 8small big-9 < -2

Representing a linear inequality on number line

Inequality Description Number line List of integer

x > 0 X is greater than 0 0 1 2 3 4 5 6

1,2,3,4,5,6………..

x > 5

x 2x is greater or

equal to 2 1 2 3 4 5 6 7

2,3,4,5,6,7…….

x -3

x < 8

x 5

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Module PMR

Representing the simultaneous linear inequalities on number line

Description Number line List of integer

-4 -3 -2 -1 0 1 2 3

-3,-2,-1,0,1,2,3

-5 -4 -3 -2 -1 0 1 2

-2 -1 0 1 2 3 4 5

0 1 2 3 4 5 6 7

2,3,4,5

3 4 5 6 7 8 9 10

-5 -4 -3 -2 -1 0 1 2

-2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2 3

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Solving linear inequalities

Method of solution Example

x - 3 < 7x - 3 < 7x < 7 + 3x < 10

x - 5 < 2

x - 2 < -6

x - 9 3

x + 2 > 5x + 2 > 5x > 5 + 2x > 7

x + 5 < -1

x + 7 -3

x + 8 7

x > 5 x 2x > 10

2x > 8

4x < -20

-2x > 10

-x < 3

-3x > 12

-5x -15

7 – x > 4

-x > 4 -7-x > -3

x < x < 3

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Module PMR

1 – 5x > -9

2x + 5 > 9

4 - 3x 16

Questions based on PMR Format1. a) Solve the inequality 2 + x ≤ 5.

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Module PMR

b) List all the integer value of x which satisfy both the inequalities – 3 ≤ 1

and 3 – x ≤ 0.

2. Solve the inequality 7 - 5x ≤ 6 – x .

3. List all integer values of x which satisfy both the inequalities ≤ 1 and

1 – 2x ≤ 5.

4. Solve each of the following inequalities : a) w – 6 ≤ 2 b) 8 + 4v ≥ 9 – 2v

5. List all the integer values of p which satisfy both the inequalities p + 3 ≤ 5 and 2 – 3p ≤ 8

6. List all the integer values of m which satisfy both the inequalities -3m ≤ 6 and 3(m-1) ≤ 2m.

7. List all integer values of x which satisfy both the inequalities 4x -2 ≤ 14 and x + 3 ≤ 2x + 5.

8. List all the integer values of x that satisfy both the inequalities 6x + 4 ≤ 5x + 7

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Module PMR

and 5 – x ≤ 6

9. List all the integer values of m that satisfy both the inequalities 2m – 1 ≤ 5 and -3m ≤ 9.

10. a) Solve the inequality 2x -1 ≥ 13. b) List all the integer value of y which satisfy both the inequalities

- 2 ≤ 1 and 3 – y ≤ 0.

11. Solve each of the following inequalities a) b) 6 – y ≤ 2y + 12

12. a) Solve the inequality m + 3 ≤ 5. b) List all the integer values of x which satisfy both the inequalities 3x – 5 ≤ 1

and 2 – n ≤ 4.

PMR past year questions

2004Linear Inequalities 59

Module PMR

1). (a). Solve the inequality .

(b). List all the integer values of which satisfy both the inequalities

and .( 4 marks )

Answer:

(a).(b).

2005

2). Solve the inequality .( 2 marks )

Answer:

2006

3). List all the integer values of which satisfy both the inequalities and

( 3 marks )

Answer:

2007

4). Solve each of the following inequalities:(a). (b).

( 3 marks )Answer:

2008 5). List all the integer values of which satisfy both the inequalities

and .( 3 marks )

Answer:

CHAPTER 5 : LINEAR INEQUALITIESANSWERS

Description Number line List of integer

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Module PMR

-4 -3 -2 -1 0 1 2 3

-3,-2,-1,0,1,2,3

-5 -4 -3 -2 -1 0 1 2 -4,-3,-2,-1,0

-2 -1 0 1 2 3 4 5

-2,-1,0,1,2,3

0 1 2 3 4 5 6 7

2,3,4,5

3 4 5 6 7 8 9 105,6,7,8

-5 -4 -3 -2 -1 0 1 2 -4,-3,-2,-1

-2 -1 0 1 2 3 4 5 -2,-1,0,1,2

-4 -3 -2 -1 0 1 2 3

-2,-1,0,1

Method of solution Example

x - 5 < 2

x - 2 < -6

x - 9 3

x + 5 < -1

x + 7 -3

Linear Inequalities 61

Module PMR

x + 8 7

2x > 8

4x < -20

-x < 3

-3x > 12

-5x -15

1 – 5x > -9

2x + 5 > 9

4 - 3x 16

Questions based on PMR Format

1. a). x 3 b). x = 4,5,6,7,8.

2. x

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Module PMR

3. x = -1,0,1,2

4. a). w ≤ 8

b). y ≥

5. x = -2,-1,0,1,2

6. m = -1,0,1,2,3

7. x = -1,0,1,2,3,4

8. x = -2,-1,0,1,2

9. m = -3,-2,-1,0,1,2

10. a). x ≥ 7 b). y = 3,4

11. a). m ≥ 7 b). y ≥ -2

12. a). m ≤ 2 b). n = -4,-3,-2,-1,0,1

13. a). x ≤ -4 b). x = -3,-2,-1,0,1,2

PMR past year questions2004 2005

1). (a). 2).

(b). and Integer

2006 2007

3). and 4). (a).

Integer (b).

20085). and

Integer

Linear Inequalities 63