Maths / Inequalities

Inequalities

= less than

= less than or equal to

= greater than

= greater than or equal to

Example: Insert the correct sign between the numbers

1. 3 7

2. 14 9

3. -3.1 -5

4. 2.06 1.9

5. -16 -9

Answers

1. 3 7

2. 14 9

3. -3.1 .5

4. 2.06 1.9

5. -16 .9

Solving Inequalities

Example: Find the value of x which satisfies:

4x – 2 18

4x 18 + 2

4x 20

x

x 5

Practice Questions

Find the values of x which satisfies each inequality:

1. 2x + 1 7

2. 10x – 2 -5

3. -2 +3x -22

4. 2.5x – 9 15

Answers

1. 2x + 1 7

2x 7 -1

2x 6

x

x 3

2. 10x - 2 - 5

10x 5 + 2

10x - 3

x -

x - 0.3

3. -2 + 3x - 22

3x – 2 - 22

3x - 22 + 2

3x - 20

x -

4. 2.5x – 9 15

2.5x 15 + 9

2.5x 24

x

x 9.6

Inequalities with a “negative x”

Examples:

1. -3x = 6 18

-3x 18 – 6

-3x 12

-x

-x 4

Change everything (negative to positive / greater than to less than etc)

x - 4

2. -4x – 5 19

-4x 19 + 5

-4x 24

-x

-x 6

Change everything

x – 6

Practice Questions:

Solve for x :

1. -5x + 7 22

2. -4x – 8 24

3. -9x – 1 17

4. -11x + 11 22

Answers

1. -5x + 7 22

-5x 22 – 7

-5x 15

-x

-x 3

x -3

2. -4x – 8 24

-4x 24 + 8

-4x 32

-x

-x 8

x -8

3. -9x – 1 17

-9x 17 + 1

-9x 18

-x

-x 2

x –2

4. -11x + 11 22

-11x 22 + 11

-11x 33

-x

-x 3

x -3

Harder Practice Questions : an x on both sides

1. 3x + 7 x + 11

2. 4x – 5 2x – 3

3. -3x + 7 x – 1

4. -4x + 6 - 5x + 10

5. -2x + 9 3x + 19

Answers:

1. 3x + 7 x + 11

3x –x + 7 11

2x + 7 11

2x 11 – 7

2x 4

x

x 2

2. 4x – 5 2x – 3

4x – 2x - 5 - 3

2x – 5 - 3

2x - 3 + 5

2x 2

x 1

3. -3x + 7 x – 1

-3x – x + 7 -1

-4x + 7 x – 1

-4x -1 – 7

-4x -8

-x

-x -2

x 2

4. -4x + 6 - 5x + 10

-4x + 5x + 6 10

x + 6 10

x 10 – 6

x 4

5. -2x + 9 3x + 19

-2x – 3x + 9 19

-5x + 9 19

-5x 19 – 9

-5x 10

-x

-x 2

x -2

Some More Difficult Questions:

1. + 5

2. 3(x + 2) + 4 (x + 5) 96

3. -

4. - -3

5. 4 (x – 1) + 5 (x + 2) -12

6. -5 (x + 1) – 6 (x + 7) -47

Answers:

1. + 5

+

9x + 8x 30

17x 30

x

2. 3(x + 2) + 4 (x + 5) 96

3x + 6 + 4 x + 20 96

7x + 26 96

7x 96 – 26

7x 70

x 10

3. -

-

4x – 6x 4

2x 4

-x

-x 2

-x -2

4. - -3

-

12x – 18x -24

-6x -24

-x

-x - 4

x 4

5. 4 (x – 1) + 5 (x + 2) -12

4x – 4 + 5x + 10 -12

9x + 6 -12

9x -12 – 6

9x -18

x + -2

6. -5 (x + 1) – 6 (x + 7) -47

-5x -5 – 6x - 42 -47

-11x - 47 -47

-11x -47 + 47

-11x 0

-x 0

x 0