Exercise 4.4 - Q1
Textbook Exercise Problem
Set up an equation and solve: Add 4 to eight times a number; you get 60.
Step-by-Step Verified Solution:
- Step 1: Let the unknown number be x.
- Step 2: Eight times the number = 8x. Adding 4 gives 8x + 4.
- Step 3: Equate to 60: 8x + 4 = 60.
- Step 4: Transpose 4: 8x = 60 - 4 = 56.
- Step 5: Divide by 8: x = 56 / 8 = 7.
Final Answer: Equation: 8x + 4 = 60, Solution: x = 7
Key Concept / Exam Strategy: Translate verbal phrases sequentially into mathematical operations.
Generated Exercise #1
Foundation
Question: Solve: 3(n - 5) = 21.
Core Concept Tested: Bracket division transposition
Mentor Hint: Divide both sides by 3 first.
Step-by-Step Solution:
- Step 1: Divide by 3: n - 5 = 21 / 3 = 7.
- Step 2: Transpose -5: n = 7 + 5 = 12.
Verified Answer: n = 12
Generated Exercise #2
Intermediate
Question: Solve for x: 4 + 5(p - 1) = 34.
Core Concept Tested: Multi-term linear simplification
Mentor Hint: Transpose 4, then divide by 5.
Step-by-Step Solution:
- Step 1: 5(p - 1) = 34 - 4 = 30.
- Step 2: p - 1 = 30 / 5 = 6.
- Step 3: p = 6 + 1 = 7.
Verified Answer: p = 7
Generated Exercise #3
Intermediate
Question: Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?
Core Concept Tested: Word problem translation to linear form
Mentor Hint: Let Parmit marbles = m. 5m + 7 = 37.
Step-by-Step Solution:
- Step 1: 5m + 7 = 37.
- Step 2: 5m = 37 - 7 = 30.
- Step 3: m = 30 / 5 = 6 marbles.
Verified Answer: Parmit has 6 marbles
Generated Exercise #4
JEE-NEET Foundation
Question: The perimeter of a rectangle is 154 m. Its length is 2 m more than twice its breadth. What are the length and breadth of the rectangle?
Core Concept Tested: Simultaneous geometric constraints in single variable
Mentor Hint: Let breadth = b, length = 2b + 2. P = 2(l + b) = 154.
Step-by-Step Solution:
- Step 1: P = 2[(2b + 2) + b] = 154.
- Step 2: 2(3b + 2) = 154 => 3b + 2 = 77.
- Step 3: 3b = 75 => b = 25 m.
- Step 4: Length l = 2(25) + 2 = 52 m.
Verified Answer: Length = 52 m, Breadth = 25 m
Generated Exercise #5
Advanced HOTS
Question: Solve for x: (2x - 3) / 4 - (x - 1) / 3 = 1.
Core Concept Tested: Rational linear equation with LCM clearance
Mentor Hint: Multiply entire equation by LCM(4, 3) = 12.
Step-by-Step Solution:
- Step 1: Multiply by 12: 3(2x - 3) - 4(x - 1) = 12.
- Step 2: Expand: 6x - 9 - 4x + 4 = 12.
- Step 3: Combine terms: 2x - 5 = 12 => 2x = 17 => x = 17/2 = 8.5.
Verified Answer: x = 17/2 (or 8.5)