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Grade 7 - Mathematics6.30 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 - Mathematics6.30 Properties of Inequalities - I

 Q 1: 6x - 6 > 2x + 2 x > 2x > -2x < 2 Q 2: 3m - 7 > 4m + 1m < -8-8 < mm < 8 Q 3: x - 2 > 6x > 8x > 6x < 8 Q 4: x + 2 > 3x > -1x > 1x < 1 Q 5: 2c + 4 > c + 4c > 0c < 4c < 0 Q 6: 2 > n + 2n > 0n < 4n < 0 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!