Simple Equations
A simple equation is a mathematical statement that says two things are equal. It contains a variable (unknown number) that you need to find. Solving an equation means finding the value of the variable that makes the statement true.
In Class 5, you learn to solve equations with one variable using basic operations — addition, subtraction, multiplication, and division. This is the first step towards algebra.
Equations are like puzzles: if x + 7 = 15, you need to find the number that, when added to 7, gives 15. That number is 8.
What is Simple Equations - Class 5 Maths (Patterns and Algebra)?
An equation is a mathematical sentence with an equals sign (=) stating that two expressions have the same value.
Examples:
- x + 5 = 12 (the value of x that satisfies this is 7)
- 3n = 24 (the value of n is 8)
- y − 9 = 16 (the value of y is 25)
Parts of an equation:
- Left-hand side (LHS) — the expression to the left of =
- Right-hand side (RHS) — the expression to the right of =
- Variable — the unknown (x, n, y, etc.)
Simple Equations Formula
To solve an equation, perform the inverse (opposite) operation on both sides.
| If the equation has | Use the inverse |
|---|---|
| Addition (+) | Subtract (−) |
| Subtraction (−) | Add (+) |
| Multiplication (×) | Divide (÷) |
| Division (÷) | Multiply (×) |
Solved Examples
Example 1: Example 1: Addition Equation
Problem: Solve x + 9 = 17
Solution:
Step 1: x + 9 = 17
Step 2: Subtract 9 from both sides: x = 17 − 9
Step 3: x = 8
Check: 8 + 9 = 17 ✓
Answer: x = 8
Example 2: Example 2: Subtraction Equation
Problem: Solve y − 14 = 23
Solution:
Step 1: y − 14 = 23
Step 2: Add 14 to both sides: y = 23 + 14
Step 3: y = 37
Check: 37 − 14 = 23 ✓
Answer: y = 37
Example 3: Example 3: Multiplication Equation
Problem: Solve 6n = 42
Solution:
Step 1: 6n = 42
Step 2: Divide both sides by 6: n = 42 ÷ 6
Step 3: n = 7
Check: 6 × 7 = 42 ✓
Answer: n = 7
Example 4: Example 4: Division Equation
Problem: Solve x ÷ 5 = 9
Solution:
Step 1: x ÷ 5 = 9
Step 2: Multiply both sides by 5: x = 9 × 5
Step 3: x = 45
Check: 45 ÷ 5 = 9 ✓
Answer: x = 45
Example 5: Example 5: Two-Step Equation
Problem: Solve 2x + 3 = 15
Solution:
Step 1: Subtract 3 from both sides: 2x = 15 − 3 = 12
Step 2: Divide both sides by 2: x = 12 ÷ 2 = 6
Check: 2(6) + 3 = 12 + 3 = 15 ✓
Answer: x = 6
Example 6: Example 6: Equation with Larger Numbers
Problem: Solve 125 + y = 300
Solution:
Step 1: y = 300 − 125 = 175
Check: 125 + 175 = 300 ✓
Answer: y = 175
Example 7: Example 7: Cricket Runs Problem
Problem: Aman scored some runs. After scoring 35 more runs in the second innings, his total became 92. Find his first innings score.
Solution:
Let first innings score = x
Equation: x + 35 = 92
x = 92 − 35 = 57
Answer: Aman scored 57 runs in the first innings.
Example 8: Example 8: Cost Problem
Problem: Priya buys 4 notebooks. The total cost is ₹120. Find the cost of one notebook.
Solution:
Let cost of one notebook = ₹n
Equation: 4n = 120
n = 120 ÷ 4 = 30
Answer: One notebook costs ₹30.
Example 9: Example 9: Two-Step Word Problem
Problem: Kavi thinks of a number. He multiplies it by 3 and adds 7. The result is 28. Find the number.
Solution:
Let the number = x
Equation: 3x + 7 = 28
Step 1: 3x = 28 − 7 = 21
Step 2: x = 21 ÷ 3 = 7
Check: 3(7) + 7 = 21 + 7 = 28 ✓
Answer: The number is 7.
Example 10: Example 10: Sharing Equally
Problem: Aditi divides her marbles equally among 6 friends. Each friend gets 8 marbles. How many marbles did Aditi have?
Solution:
Let total marbles = m
Equation: m ÷ 6 = 8
m = 8 × 6 = 48
Answer: Aditi had 48 marbles.
Key Points to Remember
- An equation has an equals sign (=) and contains at least one variable.
- To solve, use the inverse operation to isolate the variable.
- Addition ↔ Subtraction, Multiplication ↔ Division.
- Always check your answer by substituting it back into the original equation.
- Two-step equations require performing two inverse operations in order.
- The value that satisfies the equation is called the solution.
Practice Problems
- Solve: x + 23 = 50
- Solve: y − 18 = 27
- Solve: 7n = 63
- Solve: m ÷ 4 = 12
- Solve: 3x + 5 = 26
- Ria thinks of a number. She subtracts 15 and gets 42. What was the number?
- 5 bags of rice cost ₹750. Find the cost of one bag.
- Solve: 2y − 8 = 22
Frequently Asked Questions
Q1. What is a simple equation?
A simple equation is a mathematical statement with an equals sign that contains one variable. Solving the equation means finding the value of that variable.
Q2. How do you solve an equation?
Use the inverse (opposite) operation to isolate the variable. If the equation has addition, subtract. If it has multiplication, divide. Always perform the same operation on both sides.
Q3. What is the difference between an equation and an expression?
An equation has an equals sign (like x + 5 = 12). An expression does not have an equals sign (like x + 5). You solve equations but evaluate expressions.
Q4. Why should you check your answer?
Checking ensures your solution is correct. Substitute the value back into the original equation. If LHS = RHS, the answer is correct.
Q5. What is a two-step equation?
A two-step equation requires two operations to solve. For example, 2x + 3 = 11 requires first subtracting 3, then dividing by 2.
Q6. Can an equation have no solution?
At the Class 5 level, all equations you encounter will have exactly one solution. In higher classes, you will learn about equations with no solution or infinite solutions.
Q7. What is the LHS and RHS of an equation?
LHS is the Left-Hand Side (before the equals sign). RHS is the Right-Hand Side (after the equals sign). A correct solution makes LHS equal to RHS.
Q8. Can you solve equations by trial and error?
Yes, for simple equations you can try different values until you find the one that works. However, using inverse operations is faster and more reliable, especially for larger numbers.
