Algebraic Expression – Explanation & Examples

Algebra is an interesting and enjoyable branch of mathematics in which numbers, shapes and letters are used to express problems. Whether you are learning algebra in school or you are examining a certain test, you will notice that almost all mathematical problems are represented in words.

Therefore, the need of translating written word problems into algebraic expressions arises when we need to solve them.

Most of the algebraic word problems consist of real-life short stories or cases. Others are simple phrases such as the description of a math problem. Well, in this article we will learn how to write algebraic expressions from simple word problems, then advance to lightly complex word problems.

What is an Algebraic Expression?

Many people interchangeably use algebraic expression and algebraic equations unaware that these terms are totally different.

An algebraic is a mathematical phrase where two side of the phrase are connected by an equal sign (=). For example, 3x + 5 = 20 is an algebraic equation where 20 represents the right-hand side (RHS) and 3x +5 represents the left-hand side (LHS) of the equation.

On the other hand, an algebraic expression is a mathematical phrase where variables and constants are combined using the operational (+, -, × & ÷) symbols.  An algebraic symbol lacks the equal (=) sign. For example, 10x + 63 and 5x – 3 are examples of algebraic expressions.

Let’s take a review of the terminologies used in an algebraic expression:

  • A variable is a letter whose value is unknown to us. For example, x is our variable in the expression: 10x + 63.
  • The coefficient is a numerical value used together with a variable. For example, 10 is the variable in the expression 10x + 63.
  • A constant is a term which has a definite value. In this case, 63 is the constant in an algebraic expression, 10x + 63.

There are several types of algebraic expressions but the main type includes:

  • Monomial algebraic expression

This is a type of expression having only one term for example, 2x, 5x 2 ,3xy, etc.

  • Binomial expression

An algebraic expression having two unlike terms, for example, 5y + 8, y+5, 6y3 + 4, etc.

  • Polynomial expression

This is an algebraic expression with more than one term and with non -zero exponents of variables. An example of a polynomial expression is ab + b c + ca, etc.

Other types of algebraic expressions are:

  • Numeric Expression:

A numerical expression only consists of numbers and operators. No variable is added in a numeric expression. Examples of numeric expressions are; 2+4, 5-1, 400+600, etc.

  • Variable Expression:

This I an expression which contains variables alongside numbers, for example, 6x + y, 7xy+6, etc.

How to Solve Algebraic Expression?

The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation and therefore, it becomes easier to solve for the unknown terms.

To solve an equation, place the variables on one side and the constants on the other side. The variables can be isolated by applying arithmetic operations like addition, subtraction, multiplication, division, square root, cube root etc.

An algebraic expression is always interchangeable. This implies that, you can rewrite the equation by interchanging the LHS and RHS.


Example 1

Calculate the value of x in the following equation

5x + 10 = 50


Given Equation as 5x + 10 = 50

  • Isolate the variables and the constants;
  • You can keep the variable on the LHS and the constants on the RHS.

5x = 50-10

  • Subtract the constants;

5x = 40

Divide both sides by the coefficient of the variable;

x = 40/5 = 8

Therefore, the value of x is 8.


Example 2

Find the value of the y when 5y + 45 = 100


Isolate the variables from the constants;

5y = 100 -45

5y = 55

Divide both sides by the coefficient;

y = 55/5

y= 11

Example 3

Determine the value of variable in the following equation:

2x + 40 = 30


Separate the variables from the constants;

2x = 30 – 40

2x = -10

Divide both sides by 2;

x = -5


Example 4

Find t when 6t + 5 = 3


Separate the constants from the variable,

6t = 5 -3

6t = -2

Divide both sides by the coefficient,

t = -2/6

Simplify the fraction,

t = -1/3


Practice Questions

1. If x = 4 and y = 2, solve for the following expressions:

a. 2y + 4

b. 10x + 40y;

c. 15y – 5x

d. 5x + 7

e. 11y + 6

f. 6x – 2

g. 8y – 5

h. 60 – 5x – 2y

2. Sam feed his fish the same amount of food (let equal to x) thrice a day. How much food will he feed the fish in a week?

3. Nina baked 3 cupcakes for her sister and 2 cupcakes for each of her friends (let equal to x). How many cupcakes did she bake in all?

4. Jones have 12 cows at his farm. Most of the cows give 30 liters of milk per day (let equal to x). How many cows does not give 30 liters of milk per day?

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