lesson park

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

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

Something like: x < 5 or: y ≥ 11

We call that "solved".

Example: x + 2 > 12Subtract 2 from both sides:

x + 2 − 2 > 12 − 2

Simplify:

x > 10

Solved!

< becomes >

> becomes <

≤ becomes ≥

≥ becomes ≤

Add (or subtract) a number from both sides

Multiply (or divide) both sides by a positive number

Simplify a side

3x < 7+3

We can simplify 7+3 without affecting the inequality:

3x < 10

We can often solve inequalities by adding (or subtracting) a number from both sides

Example: x + 3 < 7

If we subtract 3 from both sides, we get:

x + 3 − 3 < 7 − 3   

x < 4

And that is our solution: x < 4

In other words, x can be any value less than 4

If we subtract 5 from both sides, we get:

12 − 5 < x + 5 − 5    

7 < x

That is a solution!

But it is normal to put "x" on the left hand side ...

... so let us flip sides (and the inequality sign!):

x > 7

Do you see how the inequality sign still "points at" the smaller value (7) ?

And that is our solution: x > 7