INEQUALITIES

This sign < means is less than. While this sign > means is greater than. In each case, the sign opens towards the larger number.

Example:

2 < 5 which mean 2 is less than 5. 

Equivalently, 5 > 2 which also mean 5 is greater than 2.

These are the two senses of an inequality:

< And >

Symbol	words	example
>	greater than	X + 3 > 2
<	less than	7x < 28
≤	greater than or equal to	5 ≤ x - 1
≥	less than or equal to	2y + 1 ≥ 7

Solving

Our aim is to have X (or any variable) on its own on the left of the inequality sign:

          Something like: x < 5

                      Or: y ≥ 11

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.

These things do not affect 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 change the direction of the inequality which “< becomes > “

• 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:

Solve X + 3 < 7

If we subtract 3 from both sides, we get

X + 3 < 7

X < 7 – 3

X < 4

And that is the solution: x < 4

In other words, x can be any values less than 4.

Questions that you can try:

1. 

 2.

 3. 

                GOODLUCK!😊😊😊