Finding the Unknown — Class 7 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Finding the Unknown" — 7 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Finding the Unknown" — 7 important questions with detailed answers for CBSE board e…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

What is a linear equation? Solve: 2x + 5 = 13.
Solve: 3x - 7 = 2 and verify the solution.
Solve: x/4 = 5. What is the value of x?
Form an equation and solve: Five times a number decreased by 3 is 22. Find th…
Solve: 2(x + 3) = 16 and verify.
Solve the equation: (x - 4)/3 = 2 and check your answer.
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
What is a linear equation? Solve: 2x + 5 = 13.	✓ Solved
Solve: 3x - 7 = 2 and verify the solution.	✓ Solved
Solve: x/4 = 5. What is the value of x?	✓ Solved
Form an equation and solve: Five times a number decreased…	✓ Solved
Solve: 2(x + 3) = 16 and verify.	✓ Solved
Solve the equation: (x - 4)/3 = 2 and check your answer.	✓ Solved

Showing 6 of 7 questions

Q1: What is a linear equation? Solve: 2x + 5 = 13.

Linear Equation: Definition: A linear equation is an equation of the first degree where the variable(s) have a power of 1. It is called "linear" because when plotted on a graph, it forms a straight line. Standard form (one variable): ax + b = c Where a, b, c are constants and x is the variable (a ≠ 0) Examples: • 2x + 5 = 13 • 3x - 7 = 2 • x + 10 = 25 • 5x = 20 --- Solving: 2x + 5 = 13 Step 1: Identify the equation 2x + 5 = 13 We need to find the value of x that makes this equati...

Q2: Solve: 3x - 7 = 2 and verify the solution.

Solving: 3x - 7 = 2 Step 1: Add 7 to both sides 3x - 7 + 7 = 2 + 7 3x = 9 Explanation: The inverse of subtraction is addition. We add 7 to both sides to isolate the term with x. Step 2: Divide both sides by 3 3x ÷ 3 = 9 ÷ 3 x = 3 Explanation: The inverse of multiplication is division. We divide by 3 to isolate x. --- Step 3: Verify the solution Substitute x = 3 back into the original equation: 3(3) - 7 = 2 9 - 7 = 2 2 = 2 ✓ (True) The solution is verified! --- Answer: x = 3 --- Soluti...

Q3: Solve: x/4 = 5. What is the value of x?

Solving: x/4 = 5 Step 1: Identify the operation The variable x is being divided by 4. x/4 = 5 This means: x ÷ 4 = 5 Step 2: Use the inverse operation The inverse of division is multiplication. Multiply both sides by 4: (x/4) × 4 = 5 × 4 x = 20 Explanation: When we multiply x/4 by 4, we get: (x/4) × 4 = x × (4/4) = x × 1 = x Step 3: Verify the solution Substitute x = 20 back into the original equation: 20/4 = 5 5 = 5 ✓ (True) The solution is correct! --- Answer: x = 20 --- Alternative Me...

Q4: Form an equation and solve: Five times a number decreased by 3 is 22. Find the number.

Problem: Five times a number decreased by 3 is 22. Find the number. --- Step 1: Define the variable Let x = the unknown number Step 2: Form the equation Break down the sentence: • "Five times a number" = 5x • "decreased by 3" = minus 3 = - 3 • "is 22" = = 22 Equation: 5x - 3 = 22 --- Step 3: Solve the equation 5x - 3 = 22 Add 3 to both sides: 5x - 3 + 3 = 22 + 3 5x = 25 Divide both sides by 5: 5x ÷ 5 = 25 ÷ 5 x = 5 --- Step 4: Verify the solution Substitut...

Q5: Solve: 2(x + 3) = 16 and verify.

Solving: 2(x + 3) = 16 Step 1: Expand the bracket (distribute the 2) 2(x + 3) = 2·x + 2·3 2x + 6 = 16 Explanation: Distributive property: a(b + c) = ab + ac Step 2: Subtract 6 from both sides 2x + 6 - 6 = 16 - 6 2x = 10 Step 3: Divide both sides by 2 2x ÷ 2 = 10 ÷ 2 x = 5 --- Step 4: Verify the solution Substitute x = 5 back into the original equation: 2(5 + 3) = 16 2(8) = 16 16 = 16 ✓ (True) The solution is verified! --- Answer: x = 5 --- Alternative Method (Without Expanding): Orig...

Q6: Solve the equation: (x - 4)/3 = 2 and check your answer.

Solving: (x - 4)/3 = 2 Step 1: Identify the operation The expression (x - 4) is being divided by 3. Step 2: Multiply both sides by 3 [(x - 4)/3] × 3 = 2 × 3 x - 4 = 6 Explanation: When we multiply (x - 4)/3 by 3, the division by 3 is canceled. [(x - 4)/3] × 3 = (x - 4) × (3/3) = (x - 4) × 1 = x - 4 Step 3: Add 4 to both sides x - 4 + 4 = 6 + 4 x = 10 Step 4: Check (Verify) the solution Substitute x = 10 back into the original equation: (10 - 4)/3 = 2 6/3 = 2 2 = 2 ✓ (True) The solution is ...

Showing 6 of 7 questions. Visit the full page for complete solutions.