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### Grade 7 - Mathematics6.31 Properties of Inequalities - II

Examples:
1. Consider the inequality 14 < 16
Multiplying both sides by 2m we get,
L.H.S. = 14 * 2 = 28
R.H.S. = 16 * 2 = 32
Since 14 < 16, 16 lies to right of 14.
After multiplying both sides by 2.
16 * 2 = 32 lies the right of 14 * 2 = 28.
\ 28 < 32
i.e., If 14 < 16 then 14* 2 < 16 * 2.

2. Consider the inequality 14 > 10
Multiplying both sides by 1/2, we get
L.H.S. = 14 * 1/2 = 7
R.H.S. = 10 * 1/2 = 5
Since 14 > 10, 14 lies to the right of 10.
After multiplying both sides of the inequality by 1/2,
14 * 1/2 = 7 lies the right of 10 * 1/2 = 5
\ 7 > 5.
i.e., If 14 > 10 then 14 * 1/2 > 10 * 1/2.

Multiplying (or dividing) both sides of a inequality by the same positive number does not change the order of the inequality sign.
For any three numbers a,b,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.

Example 1: Solve for x in the inequality
4x - 3 < x + 1
Adding 3 to both sides of the inequality
4x - 3 + 3 < x + 1 + 3
4x < x + 4
3x < 4 ---- dividing both sides of a inequality by 3 does not change the order of the inequality sign.
x < 4/3

Example 2: Solve for x in the inequality
x/4 < 4 ---- multiplying both sides of a inequality by 4 does not change the order of the inequality sign.
x < 16

Directions: Solve for the variable in the inequalities given below. Write at least ten examples of your own and prove the above inequality property.
 Q 1: 10x < -340x < 34x < -34x > -34 Q 2: x/12 < 2x < -24x < 24x > 24 Q 3: r/3 > 9r > 27r < 27r > -27 Q 4: x/3 > 5x > -15x < 15x > 15 Q 5: 5x < -10x > -2x < -2x < 2 Q 6: x/6 > 7x < 42x > 42x > 13 Q 7: 9x < -81x < 9x > -9x < -9 Q 8: x/8 > 9x > -72x < 72x > 72 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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