Linear Equations Solved Problems (With Step-by-Step Solutions)
Linear equations are algebraic equations in which the highest power of the variable is one. These equations form the foundation of algebra and are essential for solving advanced mathematical problems in higher classes.
In this article, you will learn how to solve linear equations in one variable through fully explained solved problems. Each example is designed to build clarity and confidence for exams.
Important Concepts
- A linear equation has the form ax + b = 0
- The goal is to isolate the variable on one side
- The same operation must be applied to both sides
- Variables represent unknown values
Solved Linear Equation Problems
Problem 1: Solve x + 7 = 15
Solution:
Step 1: Subtract 7 from both sides.
x + 7 − 7 = 15 − 7
x = 8
Solution: x = 8
Problem 2: Solve 3x = 27
Solution:
Step 1: Divide both sides by 3.
3x ÷ 3 = 27 ÷ 3
x = 9
Solution: x = 9
Problem 3: Solve 2x + 5 = 17
Solution:
Step 1: Subtract 5 from both sides.
2x = 12
Step 2: Divide both sides by 2.
x = 6
Solution: x = 6
Problem 4: Solve 4(x − 2) = 20
Solution:
Step 1: Expand the bracket.
4x − 8 = 20
Step 2: Add 8 to both sides.
4x = 28
Step 3: Divide by 4.
x = 7
Solution: x = 7
Problem 5: The sum of a number and 12 is 30. Find the number.
Solution:
Let the number be x.
x + 12 = 30
Subtract 12 from both sides.
x = 18
Required number = 18
Common Mistakes to Avoid
- Not performing the same operation on both sides
- Incorrect sign changes while transposing terms
- Errors in simplification
- Skipping verification
Practice Tips
✔ Always simplify both sides step by step
✔ Verify the answer by substituting it back
✔ Solve word problems by forming equations first
👉 Related Learning Resources: