" Greater than" is a mathematical expression that is written with the symbols
The expression "greater than" is used in mathematics, specifically in a mathematical inequality. This mathematical inequality can be between numbers, unknowns, and functions of different types.
For example, to say that 5 is greater than 3, we can express it like this:
Or, we could also put it like this.
The parts of the symbol?
In general, we have three symbols to compare mathematical expressions:
• Equal (=)
• Greater than
• Smaller than
The symbols for "greater than" and "less than" are the same. The only thing that, depending on where the open part and the closed part are located, we must put the symbol in one direction or another.
There is a trick to never be confused with the signs → the open part always points to the largest number.
Interpret "greater than"
Comparing two numbers is very easy. For example, we know that 10 is greater than 2, that 3 is greater than 2, or that 21 is greater than 20. However, when mathematical functions come into play things change a bit. Let’s see an example
Suppose we want to graph that y> 8 + 2x
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 = 8 + 2x
x = -4
Therefore, the point in the Cartesian plane would be (-4,0)
if x = 0
y = 8
Therefore, the point in the Cartesian plane would be (8,0)
We can then see in the graph that the shaded area is what would correspond to the equation y> 8 + 2x
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 equals zero are – 0.3874 and 1.7208. 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 -0.3874 (we approximate it to -0.39) and 1.7208 (or 1.72).
Then we solve for the value of y when x equals zero, which is -2 (the black point on the graph). Finally, to find what the area to be shaded should be, we change x and y to 0:
As this is true, we must shade the area where the point (0,0) is located, that is, within the parabola, which is what would correspond to the inequality.