Rules of Inequalities - Algebra

* Inequality

- It is the difference of two values.

* Basic Rules of Inequalities

1. If both sides of the inequality were added or subtracted by the same value the inequality will remain.

Examples:

* 15 > 9

By adding 5 on both sides,

15 + 5 > 9 + 5

20 > 14

* 3 < 7

By subtracting 3 on both sides,

3 - 3 < 7 - 3

0 < 4

2. If we multiply or divide both sides of the given inequality by the same positive number, the inequality will not change.

Examples:

* 5 > 2

By multiplying 4 on both sides,

5(4) > 2(4)

20 > 8

* 50 < 100

By dividing 5 on both sides,

50/5 < 100/5 

10 < 20

3. If we multiply or divide both sides of the given inequality by the same negative number, the inequality sign must be altered.

Examples:

*10 > 5

By multiplying -2 on both sides,

10(-2) > 5(-2)

-20 < -10

Since the bigger the digit of a negative number the lesser its value.

* 30 < 60

By dividing -10 on both sides,

30/(-10) < 60/(-10)

-3 > -6

4. If we raise both sides of the given inequality by the same positive exponent, the inequality will not change.

Examples:

* 7 > 4

By raising both sides by the power 2,

7² > 4²

49 > 16

* 5 < 10

By raising both sides by the power 3,

5³ < 10³

125 < 100

5. If we get the same root of both sides of the given inequality, the inequality will not change.

Examples:

*16 > 9

By getting the square root of both sides

sqrt(16) > sqrt(9)

4 > 3

* 27 > 8

By getting the cube root of both sides,

27 ^ (1/3) > 8 ^ (1/3)

3 > 2

* 100 > 49

By getting the square root of both sides, 

sqrt(100) > sqrt(49)

10 > 7