Inequalities

An inequation is like an equation, but instead of an equals sign, it has a different symbol. The symbol tells us how the two sides of the inequation compare to each other.

Here are the symbols and what they mean:

< means "less than" means "greater than"

≤ means "less than or equal to" ≥ means "greater than or equal to" So, for example, the inequation 2x < 8 means "2 times x is less than 8". This tells us that x can be any number that makes the statement true. To solve for x, we can divide both sides of the inequation by 2:

2x < 8 x < 4

So x can be any number that is less than 4.

Another example is the inequation 3x + 5 ≥ 11. This means "3 times x plus 5 is greater than or equal to 11". To solve for x, we can start by subtracting 5 from both sides:

3x + 5 ≥ 11 3x ≥ 6

Then we can divide both sides by 3:

x ≥ 2

So x can be any number that is greater than or equal to 2.

I hope this helps you understand inequations!