note math form 3 - 12 inequality equations

AIRIL BIN AHMAD

Thursday, April 13, 2023

INEQUALITIES

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD

Thursday, April 13, 2023

An inequalities is an open sentence which contains the verbs “is greater than or equal to” and “is less than or equal to”.

INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

The 4 inequalities symbols are:

> means “greater than”

means “greater than or equal to”

< means “less than”

means “less than or equal to”

INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

Example :

1.

2

1

12 9>

Fill in the boxes with the symbols > or <

2. -9 -3<

3. -2 0<

4. 5.6 5>

5. 13 7

6. -7 -12

7. -3 3

8. 1 -25

9. 0.6 0.06

10.

11.

12.

3

1

3

2

6

5

5

44

3

AIRIL BIN AHMAD

Thursday, April 13, 2023

Inequality in one variableExamples : State three values of m:

1. m > 10m = 11, 12, 13 …

2. m < 2m = 1,0,-1 …

3. m ≥ -9m = -9,-8, -7, …

4. m ≤ 0m = 0, -1, -2, …

5. m > 23m =

6. m < 1m =

7. m ≥ -2m =

8. m ≤ -8m =

AIRIL BIN AHMAD

Thursday, April 13, 2023

-1 0 1 2 3 4 5 6 7 8

To represent inequalities using number line.

Example 1: x > 2

-1 0 1 2 3 4 5 6 7 8

INEQUALITIESTo represent inequalities using number line.

Example 2 : x ≥ 2

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent inequalities using number line.

Example 3: x < 2

-1 0 1 2 3 4 5 6 7 8

INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent inequalities using number line.

Example 2 : x ≤ 6

-1 0 1 2 3 4 5 6 7 8

INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

Pg 263Ex.12.4aNo. 1,2,3,4,5,7,10,11

AIRIL BIN AHMAD

Thursday, April 13, 2023

INEQUALITIES(ADD & SUBTRACT)

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities

5 x2Example 1: 52 x

3 x...5,4,3 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities

2 x3Example 2: 23 x

5 x

...2,3,4,5x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities

2 x5

Example 3:

25 x

3 x4,5,6,7... x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities:

EXERCISE:

85 . x32 .2 x49 .3 x23 .4 x

32 .5 x

23 .6 x29 .7 x

37 .8 x26 .9 x93 .0 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

5 x2Example 1: 52 x

3 xx

3

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

7 x4Example 2: 74 x

3 xx

3

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

2 x3Example 3: 23 x

5 xx

5

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities:

EXERCISE:

52 . x32 .2 x

93 .3 x125 .4 x32 .5 x

24 .6 x15 .7 x

149 .8 x26 .9 x

109 .0 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

2 x8

Example 4:

28 x

6 xx

6

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

2 x5

Example 5:

25 x

7 xx

7

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

23 x15

Example 6:

2315 x

8 xx

8

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities:

EXERCISE:

52 . x62 .2 x

73 .3 x125 .4 x32 .5 x

24 .6 x145 .7 x62 .8 x

417 .9 x1018 .0 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

INEQUALITIES(MULTIPLY & DIVISION)

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities

8 2 x2Example 1: 822 x

6 2 x6 x23 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities

18 3 x6Example 2: 1863 x

12 3 x12 x34 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve the following inequalities:

EXERCISE:

1725 . x822 .2 x297 .3 x

1734 .4 x846 .5 x

549 .6 x72310 .7 x

327 .8 x1956 .9 x933 .0 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

Negative value of unknown

5 2 x3Example 1: 532 x

2 2 x

x22

1 x

AIRIL BIN AHMAD

Thursday, April 13, 2023

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

Example 1:List all the values of x:

2 2 4 and 3 6x x 2 2 4x 2 4 2x 2 6x

6 2x 3x

3 6x 6 3x 2x

2x

AIRIL BIN AHMAD

Thursday, April 13, 2023

3x 2x

< x <BIG

NUMBER

SMALL

NUMBER

< x <

3 2

-2, -1, 0, 1, 2, 3X =

AIRIL BIN AHMAD

Thursday, April 13, 2023

Example 2:List all the values of x:

1 2 5x 2 5 1x 2 4x

4 2x 2x

3 1 8x 3 8 1x 3 9x

9 3x

1 2 5 and 3 1 8x x

3x

AIRIL BIN AHMAD

Thursday, April 13, 2023

2x 3x

< x <BIG

NUMBER

SMALL

NUMBER

< x <

2 3

-2, -1, 0, 1, 2 , 3X =

AIRIL BIN AHMAD

Thursday, April 13, 2023

EXERCISE

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x > 2 and x > 5

-1 0 1 2 3 4 5 6 7 8

Answer : x > 5

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x < 6 and x < 2

-1 0 1 2 3 4 5 6 7 8

Answer : x < 2

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x ≥ 0 and x > 4

-1 0 1 2 3 4 5 6 7 8

Answer : x > 4

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x > 2 and x > 5

-1 0 1 2 3 4 5 6 7 8

Answer : x > 5

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

SIMULTANEOUS LINEAR INEQUALITIES

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x < 6 and x > 2

-1 0 1 2 3 4 5 6 7 8

2 < x < 6

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using number line.

Example : x < 8 and x > 0

0 < x < 8

SIMULTANEOUS LINEAR INEQUALITIES

-1 0 1 2 3 4 5 6 7 8

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using difference step.

Example : x < 8 and x > 0

< X < BIG NUMBERSMALL NUMBER

< X < 80

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

To represent simultaneous linear inequalities using difference step.

Example : x < 13 and x > 7

< X < BIG NUMBERSMALL NUMBER

< X < 137

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

Solve these questions.

1. x > 2 and x < 7

2. x < 12 and x > 5

3. x > 20 and x < 32

4. x > -4 and x < 6

SIMULTANEOUS LINEAR INEQUALITIES

AIRIL BIN AHMAD

Thursday, April 13, 2023

AIRIL BIN AHMAD

Thursday, April 13, 2023

INEQUALITIESEXERCISE

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD

Thursday, April 13, 2023

Determine the solution for each of the following linear inequalities.

QUESTION NO.1

a. 2x − 1 > 9b. 6x + 2 ≤ −10c. 7 − 4x ≥ 3

d. −3 − x < −51

2

AIRIL BIN AHMAD

Thursday, April 13, 2023

List all the integer values of f that satisfy both the inequalities 3f + 4 < 5 (4 − f) and 4f − 7 ≥ 2f − 13.

QUESTION NO.2

AIRIL BIN AHMAD

Thursday, April 13, 2023

Given that x ≤ p < y satisfies both the inequalities 10 − p ≤ 6 and 5p − (3p − 7) < 31. Find the values of x and y.

QUESTION NO.3

AIRIL BIN AHMAD

Thursday, April 13, 2023

Given that k is an integer that satisfies both the inequalities

k + 3 < 7 and

3(7k − 2) ≥ 16 + 8(2k + 1). Find all the values of k.

QUESTION NO.4

1

3

AIRIL BIN AHMAD

Thursday, April 13, 2023

List all the integer values of m that satisfy both the inequalities 4m − 13 ≥ 3 (m − 1)

and 9 − ≥ 4.

QUESTION NO.5

3

m

AIRIL BIN AHMAD

Thursday, April 13, 2023

If p < e ≤ r is the solution for the

inequalities e < 12 and

3e ≤ 15 − (e + 31), find the values of p and r.

QUESTION NO.6

4

7

AIRIL BIN AHMAD

Thursday, April 13, 2023

The inequalities 4k − 1 < 3k + 13 and 20 − (3 − 2k) > 25 have the solution a < k < b. Find the values of a and b.

QUESTION NO.7

AIRIL BIN AHMAD

Thursday, April 13, 2023

Given that y is an integer that satisfies the inequalities 17 − 5y ≥ 2 and 4 − 7(y + 2) < 11. Find all the values of y.

QUESTION NO.8

AIRIL BIN AHMAD

Thursday, April 13, 2023

Determine the solution for both the inequalities 4 − 3c < 6 − c and 6c + 13 ≤ 4c + 31.

QUESTION NO.9

AIRIL BIN AHMAD

Thursday, April 13, 2023

List all the integer values of r that satisfy both the inequalities + 3 > 4 and

3 (r + 5) − 14 ≤ 28.

QUESTION NO.10

4

r

AIRIL BIN AHMAD

Thursday, April 13, 2023

List the integer values of x such that –3 < 2x – 7 ≤ 5.

QUESTION NO.11

AIRIL BIN AHMAD

Thursday, April 13, 2023

Given that 2 < 3x + 1 < 19, find

a. the least integer value of x,b. the greatest integer value of x.

QUESTION NO.12