Examples:
- 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.
- 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.
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Example:
12 - 8x < - 3x + 20
Adding 3x both sides
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.
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