Equations, Expressions And Inequalities

In algebra, the terms equations, expressions and inequalities have separate descriptions and it is extremely important for students to understand the difference between these three mathematical expressions. When you go through your higher grades, you’ll be seeing more of these terms appearing in your math subjects. When students gain a good understanding of these concepts, it makes it a lot easier for them to solve complex mathematical problems.

Equation

Any mathematical expression that consists of an equal (=) sign is a mathematical equation. It just conveys to us the fact that values, in both sides of the equals sign, is both equal or represents the same number.

Let’s take an equation for an example:

X = 6Y is the equation.

Now to confirm that this is an equation, we need to check that there is an equals sign. Yes, there is one, hence it is an equation. But if there is an inequality sign, it may not be considered an equation. For example, if you times ≤ 6Y, then it is not an equation.

And equations can have both constants and variables on either side of the equals sign. Remember that constants are values that remain the same throughout the whole problem whilst variables are values that can be substituted with other values. Variables are normally represented by a letter such as x, y, z or anything.

A mathematical equation requires many steps to arrive at a conclusion that both values are equal. Hence during the calculation process, the values of the variables may change, but not the constants.

Examples

Let’s take a look at some examples of equations:

5x – 3 = 5
x + 10 = 2x + 5
x /2 = 10

Expression

An expression doesn’t have both an equal or an unequal sign. An expression may contain both numbers and values along with basic arithmetic symbols. For example, “5 + 6” is a simple expression that doesn’t have an equal sign but has some numbers and also an arithmetic symbol. Examples of expressions are:

  • 3 + 6
  • 2b
  • 3x + 8
  • -9

Inequalities

An inequality is similar to equations, but the only difference here is there is no equal sign present, but that it consists of the inequality sign or other mathematical symbols like ‘less than’ or ‘greater than’ symbols.

Examples of inequalities are:

  • x + 6 ≠ 8

What it means here is that the value of X+6 is not equal to 8.

  • 7 > 1

Here it means that 7 is always greater than 1.

  • 9 < 9.5

9 is less than 9.5

12 less than or equal to 9 + 8 … 12 is less than or equal to 9 plus 8
c greater than or equal to 10 … c is greater than or equal to 10