note math form 3 - 12 inequality equations

AIRIL BIN AHMAD

Thursday, April 13, 2023

INEQUALITIES

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD


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

INEQUALITIES

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The 4 inequalities symbols are:

> means “greater than”

means “greater than or equal to”

< means “less than”

means “less than or equal to”

INEQUALITIES

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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

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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 =

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-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

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Example 3: x < 2

-1 0 1 2 3 4 5 6 7 8

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Example 2 : x ≤ 6

-1 0 1 2 3 4 5 6 7 8

INEQUALITIES

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

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INEQUALITIES(ADD & SUBTRACT)

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD


Solve the following inequalities

5 x2Example 1: 52 x

3 x...5,4,3 x

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2 x3Example 2: 23 x

5 x

...2,3,4,5x

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2 x5

Example 3:

25 x

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

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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

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Negative value of unknown

5 x2Example 1: 52 x

3 xx

3

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7 x4Example 2: 74 x

3 xx

3

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2 x3Example 3: 23 x

5 xx

5

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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

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2 x8

Example 4:

28 x

6 xx

6

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2 x5

Example 5:

25 x

7 xx

7

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23 x15

Example 6:

2315 x

8 xx

8

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EXERCISE:

52 . x62 .2 x

73 .3 x125 .4 x32 .5 x

24 .6 x145 .7 x62 .8 x

417 .9 x1018 .0 x

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INEQUALITIES(MULTIPLY & DIVISION)

BY AIRIL BIN AHMAD

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8 2 x2Example 1: 822 x

6 2 x6 x23 x

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18 3 x6Example 2: 1863 x

12 3 x12 x34 x

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EXERCISE:

1725 . x822 .2 x297 .3 x

1734 .4 x846 .5 x

549 .6 x72310 .7 x

327 .8 x1956 .9 x933 .0 x

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5 2 x3Example 1: 532 x

2 2 x

x22

1 x

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SIMULTANEOUS LINEAR INEQUALITIES

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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

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3x 2x

< x <BIG

NUMBER

SMALL

NUMBER

< x <

3 2

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

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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

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2x 3x

< x <BIG

NUMBER

SMALL

NUMBER

< x <

2 3

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

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EXERCISE

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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


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Example : x < 6 and x < 2

-1 0 1 2 3 4 5 6 7 8

Answer : x < 2


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Example : x ≥ 0 and x > 4

-1 0 1 2 3 4 5 6 7 8

Answer : x > 4


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Example : x > 2 and x > 5

-1 0 1 2 3 4 5 6 7 8

Answer : x > 5


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Example : x < 6 and x > 2

-1 0 1 2 3 4 5 6 7 8

2 < x < 6


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0 < x < 8


-1 0 1 2 3 4 5 6 7 8

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To represent simultaneous linear inequalities using difference step.


< X < BIG NUMBERSMALL NUMBER

< X < 80


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To represent simultaneous linear inequalities using difference step.


< X < BIG NUMBERSMALL NUMBER

< X < 137


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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


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INEQUALITIESEXERCISE

BY AIRIL BIN AHMAD

AIRIL BIN AHMAD


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

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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

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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

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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

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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

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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

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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

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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

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

QUESTION NO.9

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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

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

QUESTION NO.11

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

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

QUESTION NO.12

note math form 3 - 12 inequality equations

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