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Grade 7 - Mathematics
6.32 Properties of Inequalities - III

Examples:
  1. Consider the inequality 6 < 8.
    Multiplying both sides of the inequality by (-6).
    L.H.S. = 6 * -6 = -36
    R.H.S. = 8 * -6 = -48
    Since 6 < 8, 8 lies to the right of 6, multiplying both sides by -6.
    6 * (-6) = -36 lies to the right of 8 * (-6) = -48.
    \ -36 > -48.
    i.e., If 6 < 8, then 6 * -6 > 8 * -6
    Order of inequality reversed.
  2. Consider the inequality -3 < 8,
    Multiplying both sides of the inequality by -4.
    L.H.S. = -3 * -4 = -12
    R.H.S. = 8 * -4 = -32
    Since -3 < 8, 8 lies to the right of -3,
    Multiplying both sides by -4
    -3 * -4 = 12 lies to the right of 8 * -4 = -32
    \ -12 > -32
    i.e., If -3 < 8, then -3 * -4 > 8 * -4
    Order of inequality reversed.

    Multiplying or dividing both sides of a inequality by the same negative number reverses the order of the inequality.
    For any three numbers a, b and c where c < 0.
    1. If a < B then ac > bc and a/c > b/c.
    2. If a > B then ac < bc and a/c < b/c.

Property: If both sides of an inequation are multiplied or divided by the same negative number, the order of the resulting inequation is reversed.

Example 1:
Solve for x in the inequality:
8 < 2 - 2x
Subtrating 2 on both sides of the inequality we get
8 - 2 < 2 - 2 - 2x
6 < - 2x
Dividing both sides of the inequality with -2 reverses the inequality sign
-3 > x
x < -3

Example 2:
Solve for y in the inequality:
(-y)/4 > 7
Multiplying both sides of the inequality with 4
(-y)/4 . 4 > 7 . 4
-y > 28
Dividing both sides of with (-1) reverses the inequality sign
y < -28


Directions: Solve for the variable in the inequalities given below. Also write at least ten examples of your own.
Directions: Write at least ten examples of your own and prove the above inequality property.
Q 1: 9 < 3 - 2x
x < -3
x > -3
x < 3

Q 2: 8 - x < 64
x < 56
x > -8
x > -56

Q 3: 9 - x < 18
x > -9
x < -9
x > 9

Q 4: (-x)/2 > 7
x < 14
x > -14
x < -14

Q 5: 12 - x < 24
x > -12
x > 12
x < -12

Q 6: (-3x) - 3 < 6
x > -3
x > 3
x < -3

Q 7: (-x)/3 > 5
x < 15
x < -15
x > -15

Q 8: 7 - x < 20
x > -13
x > 13
x < -13

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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