Equations and Expressions in Math : Definition and Examples

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Definition

An Expression is a number , a variable , or a combination of numbers and variables and operation symbols. An Equation is made up of two expressions connected by an equal sign. Some examples of expressions are

5x,   2x -3 ,   3x + 2, 

2xy + 5,  xyz + x + y + z, 

x2 + 1,  y2+ y

Some examples of Equations are :

5x = 25,  2x - 3 = 9, 

2y + 5/2 = 37/2 ,

6z + 10 = -2

From Above example we understand that equations uses equality (=) sign; it is missing in expressions.

Of these given expressions, many have more than one variable. For example, 2xy + 5 have two variables. 

Difference Between Expressions and Equations: 


Expression Equation
Expression is a mathematical phrase which combines, numbers, variables and operators to shows the value of something. Equation is a mathematical statement wherein two expressions are set equal to each other.
It's result is Simplification. It's result is Solutions.
Cannot use equality (=) sign. Uses equality sign.
It has Only one side It has Two Sides
7x - 2(3x + 14) is Example of Expression 7x - 5 = 19 is Example of Equation

Let's discuss in details about equations and expressions...

  • An algebraic equation is an equality involving variables. It has an equality sign. The expression on the left of equality sign is the Left Hand Side(LHS). The expression on the right of the equality sign is the Right Hand Side(RHS).
  • In an equation , the value of the expressions on the LHS and RHS are equal. This happens to be true only for certain value of the variable. These values are the solution of equation. In  example x = 5 is the solution of equation 2x - 3 = 7. For x = 5, LHS = 2 x 5 - 3 = 7 = RHS. On the other hand x = 10 is not a solution of the equation . For x = 10 , LHS = 2 x 10 -3 = 17. This is not equal to the RHS.
  • How to find the solution of an equation ? We Assume that the two sides of the equation are balanced. We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed .

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