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Questions Per Quiz = 2 4 6 8 10

### Grade 7 - Mathematics6.34 Properties of Inequalities - V

Examples:
1. Consider the inequality 6 < 8.
Take the reciprocals of numbers on both sides.
Reciprocal of L.H.S = 1/6
Reciprocal of R.H.S = 1/8
Since 6<8 , 8 lies to the right of 6.
Take their reciprocals, 1/6 and 1/8.
1/6 is lies to the right of 1/8
\ 1/6 > 1/8
That is if 6 < 8 then 1/6 > 1/8.

2. Consider the inequality -6 > -8.
Take the reciprocals of numbers on both sides,
Reciprocal of L.H.S. = -1/6
Reciprocal of R.H.S. = -1/8
-1/6 lies to the left of -1/8.
\ -1/6 < -1/8.
That is, if -6 > -8, then -1/6 < -1/8
If a and b are the same sign and a < b (a > b) then 1/a > 1/b (1/a < 1/b).
If reciprocals are taken to quantities of the same sign on both sides of an inequality then the order of the inequality is changed.

Example:
12 - 8x < - 3x + 20
12 - 8x + 3x < - 3x + 3x + 20
12 - 5x < 20
Subtracting 12 both sides
12 - 12 - 5x < 20 - 12
- 5x < 8
Dividing both sides by -5 reverses the inequality
x > -8/5

Directions: Write at least ten examples of your own and prove the above inequality property.
 Q 1: 2 - 5r > -3r + 14r < 6r > -6r < -6 Q 2: 6x - 16 > 8x - 24x < 4x > 4x < -4 Q 3: 10 - 7x > -5x + 15x < -5/2 x > -5/2x > 5/2 Q 4: 15 - 6y > -5y + 16y < -1y < 1y > -1 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!