An equation says that two expressions have the same value. In 3x + 5 = 20, the letter x represents an unknown number. Solving the equation means finding a value of x that makes the statement true.
These examples are simple linear equations in one variable: the variable is raised only to the first power. The main idea is to keep both sides equal while making the equation easier to read.
Think of a balanced scale
If you add the same amount to both sides of a balanced scale, it stays balanced. The same idea works for an equation. You can add or subtract the same number on both sides. You can also multiply or divide both sides by the same nonzero number.
Choose an operation that undoes something around x. Addition is undone by subtraction, and multiplication by a nonzero number is undone by division. Write the operation on both sides until the process feels familiar.
Example 1: Undo addition, then multiplication
Solve 3x + 5 = 20.
Subtract 5 from both sides:
3x + 5 – 5 = 20 – 5
3x = 15
Divide both sides by 3:
3x / 3 = 15 / 3
x = 5
Check in the original equation: 3 × 5 + 5 = 15 + 5 = 20. Both sides are equal, so x = 5 is correct.
Example 2: Handle a negative answer
Solve 4x – 7 = -19.
Add 7 to both sides:
4x – 7 + 7 = -19 + 7
4x = -12
Divide both sides by 4:
x = -3
Check: 4 × (-3) – 7 = -12 – 7 = -19. A negative answer is allowed unless the context rules it out. In this equation, it works.
Example 3: Work with brackets
Solve 2(x + 3) = 18.
The entire expression x + 3 is multiplied by 2. Divide both sides by 2 first:
x + 3 = 9
Subtract 3 from both sides:
x = 6
Check: 2 × (6 + 3) = 2 × 9 = 18. You could also expand the brackets to get 2x + 6 = 18, then solve. Both methods give the same result when each operation is applied correctly.
Turn a word problem into an equation
Three identical notebooks and one ₹10 pen cost ₹100 altogether. What is the price of one notebook?
Let x be the price of one notebook in rupees. Three notebooks cost 3x rupees, so the equation is 3x + 10 = 100. Subtract 10 to get 3x = 90. Divide by 3 to get x = 30.
Write the answer with its meaning: each notebook costs ₹30. Check the total: 3 × ₹30 + ₹10 = ₹100.
Two mistakes to watch for
Avoid changing only one side of an equation. If you subtract 5 on the left, subtract 5 on the right too. Also remember that 2(x + 3) expands to 2x + 6, because 2 multiplies both terms inside the brackets.
Try these yourself
1. x + 9 = 16
2. 5x = 35
3. 2x – 4 = 10
Write your steps before checking the answers: 1) x = 7; 2) x = 7; 3) x = 7. Although the answers match, the operations differ. Substitute each answer into its own original equation to confirm your working.