# Smaller than

"Less than" is a mathematical expression that is written with the symbols.

"Less than" is used in mathematics. Specifically, in a mathematical inequality. When we talk about inequality, it can be between numbers, unknowns and functions of various kinds.

For example, if we want to say that 2 is less than 6

2 < 6

We can also express it this way:

6 > 2

The parts of the "less than" symbol?

Mainly, we have three symbols to indicate that a mathematical inequality exists:

• Equal (=)

• Greater than

• Smaller than

"Less than" and "greater than" use the same symbols. Depending on where the smallest part and the largest part are located, we must put the symbol in one direction or the other.

There is a trick to never be confused with the signs → the open part always points to the largest number.

Mathematical equality

## Interpret "less than"

Comparing numbers is easy. For example, we know that 9 is less than 12, that 5 is less than 14, or that 21 is less than 35. However, when we write equations things get a bit complicated. Let's see an example

Suppose we want to graph that y <6-3x

So, first we take the equation as an equality and we solve for those points where the variables are equal to zero

if y = 0

0 = 6-3x

x = 2

Hence, the point on the Cartesian plane would be

if x = 0

y = 6

Therefore, the point in the Cartesian plane would be

We can then observe in the graph that the shaded area is what would correspond to the equation y <6-3x

Now suppose I have the following quadratic equation:

So we first take the equation on the right and draw the parabola that corresponds when we set it equal to zero.

When we solve the equation, we find that the values of x when y is equal to zero are -0.5 and 1. So, those are the two points through which the parabola must pass as we see in the following graph (The equation can be solved in an online calculator).

On the graph, the parabola crosses the x-axis when the value of x is -0.5 and 1.

Then we solve for the value of y when x is equal to zero, which is -2. Finally, to find what the area to be shaded should be, we change x and y to 0

0 < 0-0-2

0<-2

As this is not true, we must shade the area where the point is not, that is, outside the parabola, which is what would correspond to the inequality.