What is difference between an expression and an equation in mathematics? Both use numbers and variables; however it is all based on the arrangement. So let's take look at both to determine their use and relationship. An expression is a combination of numbers, variables, and symbols to be calculated. An equation contains expressions that are separated by an equals sign.
A further look at the mathematical expression can be explained with numbers and variables such as: 7x + y  4. The only way that you solve this expression is that you need to know what the variables represent. It can be as simple as 8x  2 or as complicated as 5x(x + 2y)  (5x + 2y) + y(2x + z). In either of these expressions all you have to do is define the variables and using PEMDAS simplify and solve the problem. If you calculate the expression 5x(x + 2y)  (5x + 2y) + y(2x + z), we need to define the variables: x = 2, y = 3, z = 4. So let's solve the expression:
Expression  
5x(x + 2y)  (5x + 2y) + y(2x + z)  The Problem 
5 * 2(2 + 2 * 3)  (5 * 2 + 2 * 3) + 3(2 * 2 + 4)  Variables defined 
5 * 2(8)  (16) + 3(8)  Parentheses 
80  16 + 24  Operations 
88  Answer 
An equation is the combination of two expressions that are separated by an equals sign. So this means that both expressions must equal each other. This makes the problem relatively simple to solve, because you can solve the side that is easiest first and then solve the other side. Let's take a look at an equation and solve it: x  4 = 5. Since we know that the both expressions must equal each other, the "x" can only be a 9: 9  4 = 5, 5 = 5.
Let's take a look at a more complicated equation. x + 7 + 3(4 + 5) = (x * 12) + 12. The only way you can solve this problem without doing a lot of guessing and checking is to know the value of "x." In this case we will have x = 2. So let's solve the equation:
Equation  
expression = expression  
x + 7 + 3(4 + 5) = (x * 12) + 12  The Problem 
2 + 7 + 3(4 + 5) = (2 * 12) + 12  Variables defined 
2 + 7 + 3(9) = (24) + 12  Parentheses 
2 + 7 + 27 = 36  Addition 
36 = 36  Answer 
Let's take a look at some examples to prove that these rules are correct:
5 + 36 = 36 + 5

36  5 = 36  5

41 = 41

31 = 31

2 * 36 = 36 * 2

36 / 2 = 36 / 2

72 = 72

18 = 18

Equations and expressions are used in higher levels of mathematics that require special calculations to solve graphical problems and geometric figures. They are also used in explanations of lines, cartoons, and diagrams. They have their place in computer software and used for developing animations.