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### Grade 7 - Mathematics6.32 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 - 2xx < 3x > -3x < -3 Q 2: 8 - x < 64x > -8x > -56x < 56 Q 3: (-3x) < 9x > -3x < -3x > 3 Q 4: (-x)/2 > 7x < 14x < -14x > -14 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!