Examples:
 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.
 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.
