So, what is an inequality? An inequality is an equation wherein the two values could or could not be equal to each other, but we should know what the symbols make an inequality equation and a normal equation.

These are the four symbols that will define how an inequality question shall play out.< (less than) > (greater than) ≤ (less than or equal to) ≥ (greater than or equal to).

Usually in an inequality equation the unknown variable is on the left side of the equation with the other value is on the right, like so:

x > 5

This equation denotes that x is greater than 5, and this can be anything so long as it’s higher than 5, its obviously impossible for us to list out every single individual number that is higher than 5, so we graph it on a number line

The arrow faces wherever the inequality is, so if it’s less than it points to the left, and if it’s greater than it’s to the right. If the inequality has a dash beneath it, denoting an “or equal to” equation, then it will instead turn out like this:

The reason why the normal inequalities are open in are because they are the boundary point between what is a correct value or not, while the “or equal to” is shaded because the number is included in the values that could be the correct answer.

With that out of the way, let’s solve a normal inequality question and check if our answers are correct. Let’s say our equation is  x+2.5<-6

We do the standard legal move procedure until we find an equation where one side has the variable and the other has a value.

Afterwards we can graph it on a number line, but what we’re focusing on here is how to check if our answer is correct, so the best thing to do is plug in the answer we got into the x and solve as per usual.

This shows that our dashed inequality is correct, but we should also check if the inequality is facing the right direction, so we pick a number according to the inequality, in this case we will be using -9.

This confirms that the inequality symbol is now facing in the right direction.

That’s what I’ve learned in Grade 9 Inequalities