Algebraic equations are mathematical statements where two expressions are separated by an equal sign.

The variables can be on both sides of the equality sign. We use letters to denote variables.

Examples:

$x = 4 + 2$. Here, we observe that the variable is on one side of the equation.

$2x + 3 = x + 4$. Here, we can observe that the variables are on both sides of the equation.


An algebraic equation contains variables, numbers and an equal sign that can be interpreted into meaningful statements. These variables are also called as literal coefficients.
Any word problem can be changed into a simple and clear algebraic equation, which makes solving it much easier.

Solving a word problem depends on how well one understands it and translates it into a mathematical statement.
So, the main steps that have to be followed while dealing with a word problem are:
  • Understand what is given.
  • Understand what is to be found
  • Understand the relation between what is to be found and what is given.
Word problems get easier if you understand the keywords that are used in the problem.
Lets consider some

Operation Symbol Keyword
Addition + Sum
Added to
Total
More than
Increased by
Subtraction - Minus
Less
Difference
Decreased by
Fewer than
Multiplication * Multiplied by
Product of
Times
Of
Division ÷ Out of
Ratio of
Per
Quotient of
Percent
Equal = Is
Are
Will be
Gives
Were
Power of ^ Squared
Cubed

Algebraic equations are very useful in solving word problems as they show a symbolic way of solving them.
When reading a word problem, one must be very careful in interpreting the sentences to equations.

The following steps can be followed to convert a word problem into an algebraic equation:
  • Understand the problem by reading it thoroughly
  • Check what is to be found and assign it a variable, say x.
  • Check what is given.
  • Form an equation connecting the given values and the variable, x.
Hence, we get an equation which can be solved to get the variable.

Examples on Writing Algebraic Equations


Given below are some examples that explain how to form an algebraic equation.

Example 1:

Half of a number increased by 5 is 10

Solution:

Let the number be x.
$\frac{1}{2}$ $x + 5 = 10$

Example 2:

Jane gets 20 dollar as pocket money. How much money does she need to buy a toy that costs 92 dollars?

Solution:

Step 1: First consider what is given. Jane has 20 dollar and wants to buy a toy that costs 92 dollars. The question is how many more dollars are needed to buy the toy.

Step2: Let us call the extra amount needed as x.

Step3: So, she already she has 20. We need x more money to get 92 dollars. Hence, an equation can be formed
$20 + x = 92$

Step4: Subtract 20 from both sides
$x = 72$
So, Jane needs 72 dollars more to buy the toy.

Example 3:

The sum of 11 and a quantity is multiplied by 2 to get 8. Find the quantity.

Solution:

Let us consider the quantity as u.
Given, the sum of 11 and a quantity is multiplied by 2 to get 8.
So, the algebraic equation formed will be as follows:
$(u + 11) \times 2 = 8$

Divide both the sides by 2
$(u + 11) = 4$

Subtract 11 from both the sides
$u = 4 – 11$
u = 7 dollars