Examples:
 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.
 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.
