Among other things, this week in math we looked at inequalities. The word inequality means quite simply, that the two sides of an equation are not equal. Inequalities are used to compare values. We use the symbol “<” (less than) and “>” (greater than) to show which side is higher in value. This can be transferred to graphs relatively easily. If we know that…

y > 3 we also know that the variable “y” must be a value greater than 3. This would, on a graph, leave the entire space above y = 3 shaded in as that is the infinite space that a point could be placed.  When showing this on a graph, the line at y = 3 has to be dotted to show that the value must be higher than 3 and not 3 itself.

Now, if there’s a line underneath the symbol like “≤” then that simply means “greater than or equal to…” It just indicates that the value can also include the number itself. To demonstrate this on a graph, the line would just become solid instead of broken.

Now, when applied to linear equations, it’s actually quite simple, as our example from before (y = 3) was also linear, just more simple. Take the line y = 2x +3. It’s incredibly easy, just a straight line with a slope of 2/1 and a y-intercept of 3.

Now if we swap the equals sign for an inequality, like y ≤ 2x + 3, then all that means is that the value must be below the line.

* Another thing to always remember is that the inequality is like an arrow: with > pointing to the right on the number line, meaning it is a greater than symbol with < pointing towards the negatives on a number line meaning it is a less than symbol.