Vardaan
Class 7 Maths • Chapter 04

Simple Equations

Vardaan Learning Institute • Detailed Notes with Practice Questions

⚖️ 1. What is an Equation?

An equation is a mathematical statement that says two expressions are equal. It always has an equals (=) sign.

Expression Equation Difference
2x + 3 2x + 3 = 9 Expression has no = sign; Equation has = sign
3y − 5 3y − 5 = 10 An equation has both LHS and RHS
Parts of an Equation:
• Variable (unknown): the letter to find (x, y, n, etc.)
• LHS (Left-Hand Side): expression before the = sign
• RHS (Right-Hand Side): expression after the = sign
• Solution: the value of the variable that makes LHS = RHS (also called ROOT of the equation)

⚖️ 2. The Balance Method — Core Concept

Think of an equation as a balance scale. Both sides must stay balanced. Whatever you do to one side, do the SAME to the other side!

LHS: 2x+3 RHS: 9 Pivot = Balance point

🔑 3. Methods to Solve Equations

Method 1: Transposition (Moving terms across = sign)

🔑 Golden Rule of Transposition When you move a term from LHS to RHS (or vice versa), its sign is reversed:
• Addition ↔ Subtraction when crossing the = sign
• Multiplication ↔ Division when crossing the = sign
✏️ Solve: 2x + 5 = 13
2x + 5 = 13
2x = 13 − 5     (transposing +5 from LHS → becomes −5 on RHS)
2x = 8
x = 8 ÷ 2     (transposing ×2 from LHS → becomes ÷2 on RHS)
x = 4
✅ Check: 2(4)+5 = 8+5 = 13 ✓
✏️ Solve: 3(y − 2) = 12
3(y − 2) = 12
y − 2 = 12 ÷ 3 = 4
y = 4 + 2
y = 6
✅ Check: 3(6−2) = 3(4) = 12 ✓
✏️ Solve: (n+3)/5 = 4
(n+3)/5 = 4
n + 3 = 4 × 5 = 20     (multiply both sides by 5)
n = 20 − 3
n = 17
✅ Check: (17+3)/5 = 20/5 = 4 ✓

Method 2: Trial and Error (for simple equations)

Example: Solve 5x − 3 = 12. Try different values of x:
x=2: 5(2)−3 = 7 ≠ 12
x=3: 5(3)−3 = 12 ✓ → Solution: x = 3
(Better to use transposition for complex equations!)

📝 4. Setting Up Equations from Word Problems

Steps:
  1. Identify the unknown — give it a variable (e.g., x)
  2. Translate the words into an equation — "is" → "=", "sum" → "+", etc.
  3. Solve the equation
  4. Verify the answer in the original question

Key phrase translations:
English Phrase Mathematical Symbol/Expression
A number / some number x (or any variable)
Sum of x and 5 x + 5
5 more than x x + 5
5 less than x x − 5
x is 5 less x − 5
5 times a number 5x
A number divided by 3 x/3
Thrice a number reduced by 4 is 11 3x − 4 = 11
📝 Word Problem: "The sum of three consecutive odd numbers is 51. Find the numbers."
Let first odd number = x
Next consecutive odds: x+2 and x+4
Equation: x + (x+2) + (x+4) = 51
3x + 6 = 51
3x = 45 → x = 15
Numbers: 15, 17, 19
✅ Check: 15+17+19 = 51 ✓
✏️ Practice Questions — Simple Equations (30 Questions)

Section A — Solve the Equation Easy

Q1. x + 7 = 15
Q2. y − 9 = 4
Q3. 3n = 21
Q4. m/4 = 6
Q5. 2x + 3 = 11
Q6. 5y − 8 = 12
Q7. 3(x + 4) = 21
Q8. (n − 3)/4 = 5
Q9. 8 + 4a = 32
Q10. 2(3x − 1) = 16

Section B — Translate and Solve Medium

  1. Q11. Seven added to three times a number gives 28. Find the number.
  2. Q12. If you subtract 5 from twice a number, you get 17. Find the number.
  3. Q13. A number when divided by 4 and increased by 3 gives 8. Find the number.
  4. Q14. The sum of two consecutive numbers is 29. Find the numbers.
  5. Q15. The sum of three consecutive even numbers is 48. Find them.
  6. Q16. Raju is 7 years older than his sister. Sum of their ages is 37. Find their ages.
  7. Q17. A bag has red and blue balls. There are 3 times as many red as blue. Total balls = 48. Find the number of each colour.
  8. Q18. The perimeter of a rectangle is 40 cm. Its length is 4 more than its width. Find length and width.

Section C — Mixed Solve Medium

Q19. 4(2t − 3) = 3(3t − 2)
Q20. (x+3)/4 = (x−1)/2
Q21. 5(x − 1) + 3(x + 2) = 7
Q22. 3x + 4/3 = 5 + x
Q23. If 3x − 4 = 5, find the value of 5x + 1
Q24. If x + x/2 + x/4 = 28, find x

Section D — Challenge Hard

  1. Q25. A student's score in the 2nd term is 8 marks more than double his 1st term score. Combined total is 95. Find both scores.
  2. Q26. A father is 30 years older than his son. In 5 years, the father will be 3 times as old as the son. Find their present ages.
  3. Q27. The sum of the digits of a 2-digit number is 9. If digits are reversed, the new number is 27 more than the original. Find the number.
  4. Q28. Find x: 2(x+3) − 3(2x−4) = 5(x−7)
  5. Q29. A shopkeeper sells a pen for ₹12 and a pencil for ₹3. Shyam buys some pens and twice as many pencils, paying ₹54 in total. How many pens did he buy?
  6. Q30. In a class, ratio of boys to girls is 3:2. After 5 more boys join, the ratio becomes 4:2. Find the original number of boys and girls.
✅ Key Answers: Q1: 8 | Q2: 13 | Q3: 7 | Q4: 24 | Q5: 4 | Q6: 4 | Q7: 3 | Q8: 23 | Q9: 6 | Q10: 3 | Q14: 14 & 15 | Q15: 14, 16, 18 | Q16: Raju 22, Sister 15 | Q26: Son 10, Father 40

📝 Quick Revision

  1. An equation: Mathematical statement with LHS = RHS containing an unknown variable
  2. Solution = value that makes LHS = RHS. Always VERIFY your solution!
  3. Transposition: Move term across = sign with reversed sign (+ becomes −, × becomes ÷)
  4. Whatever you do to one side, do the SAME to the other side (balance method)
  5. For word problems: identify unknown → write equation → solve → verify
  6. Consecutive numbers: n, n+1, n+2. Consecutive even/odd: n, n+2, n+4