Home › Free notes › Class 7 Mathematics › Finding the Unknown

Finding the Unknown – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 15. Notes, key terms, important questions with answers and MCQs.

Chapter overview

An equation says two expressions are equal. Solving it means finding the value of the unknown that makes it true, by doing the same operation on both sides.

Solving equations

Keep the balance: whatever you do to one side, do to the other.
x + 5 = 12 → x = 7; 3x = 21 → x = 7; x/4 = 5 → x = 20.
Two-step: 2x + 3 = 15 → 2x = 12 → x = 6.

From words to equations

"A number increased by 8 is 20": x + 8 = 20.
"Three times a number minus 4 is 11": 3x − 4 = 11.
Always check by substituting the answer.

Key terms

Equation: statement that two expressions are equal
Solution: value of the variable that makes the equation true
Transposing: moving a term to the other side of an equation with the opposite sign

Formulas

ax + b = c ⇒ x = (c − b)/a

Important questions with answers

Solve x/4 + 3 = 8.2 marks

x/4 = 5, so x = 20.

Write and solve: "Twice a number decreased by 5 is 23."3 marks

2x − 5 = 23, so 2x = 28 and x = 14.

Ravi's age is 3 times his son's age. After 12 years, Ravi will be twice as old as his son. Find their present ages and check the answer.5 marks

Let the son's age be x; Ravi's is 3x. After 12 years: 3x + 12 = 2(x + 12) = 2x + 24, so x = 12. Son 12 years, Ravi 36 years. Check: after 12 years, 48 = 2 × 24 ✓.

Quick revision

Do the same to both sides.
Check the answer.
Translate words carefully.

Exam tips

Undo operations in reverse order: first + or −, then × or ÷.
For ages, write the present age as x and future/past ages as x ± years.

Practice MCQs

If x − 4 = 9, then x =
1. 5
2. 13
3. 36
4. −5
Show answer
Answer: (b) 13. Add 4 to both sides.
If 5x = 35, then x =
1. 7
2. 30
3. 40
4. 175
Show answer
Answer: (a) 7. Divide by 5.
Solve 2x + 7 = 19
1. 12
2. 13
3. 6
4. 8
Show answer
Answer: (c) 6. 2x = 12.
"Four times a number is 6 more than twice the number." The number is
1. 2
2. 3
3. 6
4. 12
Show answer
Answer: (b) 3. 4x = 2x + 6.
Solve 3x − 7 = 11
1. x = 4
2. x = 6
3. x = 18
4. x = 3
Show answer
Answer: (b) x = 6. 3x = 18.
The perimeter of a rectangle is 40 cm and its length is 12 cm. Its breadth is
1. 8 cm
2. 16 cm
3. 28 cm
4. 10 cm
Show answer
Answer: (a) 8 cm. 2(12 + b) = 40.
Mohan is 5 years older than Sita. The sum of their ages is 31. Sita's age is
1. 15
2. 18
3. 13
4. 12
Show answer
Answer: (c) 13. x + x + 5 = 31.
The sum of three consecutive numbers is 51. The largest is
1. 16
2. 17
3. 18
4. 19
Show answer
Answer: (c) 18. x + x + 1 + x + 2 = 51, x = 16.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.