Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

#### Online Quiz (WorksheetABCD)

Questions Per Quiz = 2 4 6 8 10

### 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: r/3 > 9r < 27r > -27r > 27 Q 2: 10x < -340x > -34x < 34x < -34 Q 3: x/6 > 7x > 13x > 42x < 42 Q 4: x/12 < 2x < -24x < 24x > 24 Q 5: x/8 > 9x > -72x < 72x > 72 Q 6: x/3 > 1x > 3x < 3x < 1 Q 7: 5x < -25x < -5x < 5x > -5 Q 8: 5x < -10x < 2x > -2x < -2 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!