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.
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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.
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Frequently asked questions
How do you solve a simple linear equation step by step?
Identify what is being done to x, then undo it using the opposite operation. Always apply the same operation to both sides. Keep going until x is alone on one side.
How do you check if your answer to a linear equation is correct?
Put your answer back into the original equation in place of x. Work out both sides separately. If both sides give the same number, your answer is correct.
Can the answer to a linear equation be a negative number?
Yes. A negative answer is valid as long as the problem does not say otherwise. Always check by substituting it back into the original equation.
What does it mean to expand brackets in a linear equation?
It means multiplying the number outside the bracket by every term inside it. For example, 2(x + 3) becomes 2x + 6. You must multiply all terms inside, not just the first one.