Simple Equations

m = 25

Step 1: We have m/5 + 3 = 8. We need to find m. Step 2: Transpose +3 to the RHS. It becomes -3. So m/5 = 8 - 3 = 5. Step 3: Multiply both sides by 5 to remove the fraction. m = 5 × 5 = 25. Step 4: Verify: 25/5 + 3 = 5 + 3 = 8 = RHS. Correct! Common mistake: Multiplying by 5 before transposing 3, which gives m + 3 = 40, leading to m = 37.

x = 15

Step 1: We check which value satisfies 4x + 5 = 65. Step 2: Try x = 15: LHS = 4(15) + 5 = 60 + 5 = 65 = RHS. This works! Step 3: To confirm it is the only solution, solve the equation: 4x = 65 - 5 = 60, so x = 15. Step 4: Check other options: x = 10 gives 4(10)+5 = 45 ≠ 65; x = 20 gives 4(20)+5 = 85 ≠ 65. Only x = 15 satisfies the equation. This was the equation from the mind-reading game in the chapter.

6

Step 1: Let the number be x. Step 2: 'Seven times a number plus 4 equals 46' gives: 7x + 4 = 46. Step 3: Transpose +4: 7x = 46 - 4 = 42. Step 4: Divide both sides by 7: x = 42 ÷ 7 = 6. Step 5: Verify: 7(6) + 4 = 42 + 4 = 46 = RHS. The number is 6. Common mistake: Writing the equation as 7(x + 4) = 46, which gives a different answer.

y = 7

Step 1: We have 10y - 20 = 50. Step 2: Transpose -20 to the RHS. It becomes +20. So 10y = 50 + 20 = 70. Step 3: Divide both sides by 10: y = 70 ÷ 10 = 7. Step 4: Verify: 10(7) - 20 = 70 - 20 = 50 = RHS. Correct! This is the equation from Appu's mind-reading game. The answer is y = 7. Common mistake: Dividing 50 by 10 first to get y - 20 = 5, then y = 25, which is incorrect.