INEQUALITIES 2

Examples:

How to Solve

Solving inequalities is very like solving equations ... we do most of the same things ...
... but we must also pay attention to the direction of the inequality.

Direction: Which way the arrow "points".

Some things we do will change the direction!

< would become >

> would become <

≤ would become ≥

≥ would become ≤

Safe Things To Do

These are things we can do without affecting the direction of the inequality:

Add (or subtract) a number from both sides
Multiply (or divide) both sides by a positive number
Simplify a side

Example 1: 

3x < 7+3

We can simplify 7+3 without affecting the inequality:

3x < 10

But these things will change the direction of the inequality ("<" becomes ">" for example):

Multiply (or divide) both sides by a negative number
Swapping left and right hand sides

Example 2: 

2y+7 < 12

When we swap the left and right hand sides, we must also change the direction of the inequality:

12 > 2y+7

Example 3: 

2x+6 < 12

Ans = x < 3

Exercise :

Solve the following

(a) 3x < 12

(b) 2y +4 > 16