Name: ___________________

Date:___________________

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Grade 7 - Mathematics
6.30 Properties of Inequalities - I

Example:
15 > 8, adding 6 to both sides, we get
L.H.S. = 15 + 6 = 21
R.H.S. = 8 + 6 = 14
Since 15 > 8, 15 lies to the right of 8, after adding 6 to both sides 21 lies to the right of 14.
\ 21 > 14
\ If 15 > 8 then 21 > 14 ...........I

Consider 6 > -4, adding (-2) both sides, we get
L.H.S. = 6 + (-2) = 4
R.H.S. = (-4) + (-2) = -6
Since 6 > -4, 6 lies to the right of -4, after adding (-2) both sides 4 lies to the right to (-6).
\4 > -6
\ If 6 > -4 then 4 > -6 .............II

From I and II we have the property - I

Adding (or subtracting) the same number to both sides of an inequality does not change the order of the inequality sign (i.e., greater than or less than)
i.e. if a < b then a+c < b+c and a-c < b-c
Similarly,
If a > b then a+b > b+c and a-c > b-c for any three numbers a, b, and c.


Example:
Solve for x in the inequality
x - 15 > 8
x - 15 + 15 > 8 + 15 ------------ adding 15 on both sides does not change the inequality
x > 23

Directions: Write at least ten examples of your own and prove the above inequality property.

Name: ___________________

Date:___________________

Grade 7 - Mathematics
6.30 Properties of Inequalities - I

Q 1: 6x - 6 > 2x + 2
x < 2
x > 2
x > -2

Q 2: x - 2 > 6
x > 6
x > 8
x < 8

Q 3: 4r + 15 < 3r - 15
r < 15
r > 30
r < -30

Q 4: 2c + 4 > c + 4
c < 4
c < 0
c > 0

Q 5: x + 2 > 3
x < 1
x > -1
x > 1

Q 6: 2 > n + 2
n < 0
n > 0
n < 4

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Question 8: This question is available to subscribers only!


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