Download - 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
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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
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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