Rules of inequalities I

**Solving Inequalities Rules**

A mathematical expression which involves symbols >, <, ≥ and ≤ is an inequality. To solve such we need go find a range of values that an unknown variable can take and then satisfy the in-equality. The rules for solving such are that, if the same number is added to both sides of an in-equal form, the form remains true.

If the same number is subtracted from both sides of the inequality, the in-equality remains true. If multiplication is done by the positive number, the in-equality remains true. But if multiplication or division of such an form is done by a negative number, then it is no longer true. In fact, the relation becomes reversed. These are explained briefly with examples below.

**Rules for Inequalities**

While solving an such problem there are inequality rules that needs to be followed. If the form involves addition or subtraction then we add or subtract by the same number both sides in order to have the variable to one side.

For example take x – 5 > 12. Here we have -5 so we add +5 both sides and get x > 17. Take another example x +6 > 15. Here we subtract 6 both sides. We get, x > 9.

If it involves multiplying then we have to divide both sides by the same number. For example take 4x >12.

So divide by 4 both sides we get x > 3. If it involves division then we multiply both sides.

x/4 > 12. Here multiply by 4 both sides. We get x > 48.

When Multiplication is done by a negative number the sign of the in-equality should be flipped x/-3 > 12. Here we times both by -3. So x < -36. The sign of the in-equality is flipped.

The > sign is now changed to <. Similarly when we divide by a negative number we flip the sign. Take -5x > 35. Divide by -5 both sides and flip the relation. X < -7. Here also the > sign is flipped t the < sign.

While graphing inequalities if the relation has a < or > sign when we have to draw a dotted line. This indicates that the line is not a part of the solution. If the in-equality is less than, or equal to and or greater than / equal to then we use a solid line for graphing. This indicates that the line contains solutions for the inequality. These are the rules of Solving Inequalities