S2 Unit 21 Forming and Solving Equations

Apuntes

**• Understanding Dora's Mistake:** Dora has solved the equation \(3(x + 2) = 62\) but made an error in her steps. Let's analyze her work: Starting with the original equation: \[3(x + 2) = 62\] Expanding the left side: \[3x + 6 = 62\] Subtracting 6 from both sides: \[3x = 56\] Dividing both sides by 3: \[x = \frac{56}{3}\] However, Dora's solution shows: \[3x + 5 = 62\] which is incorrect because she incorrectly simplified \(3(x + 2)\) to \(3x + 5\). The correct expansion should be \(3x + 6\), not \(3x + 5\). **Main mistake:** She incorrectly expanded \(3(x + 2)\) as \(3x + 5\) instead of \(3x + 6\). --- **• Solving the Equations:** 1. \(a + 24 = 39\) \[ a = 39 - 24 = \boxed{15} \] 2. \(39 = b - 24\) \[ b = 39 + 24 = \boxed{63} \] 3. \(4c - 10 = 26\) Add 10 to both sides: \[ 4c = 26 + 10 = 36 \] Divide both sides by 4: \[ c = \frac{36}{4} = \boxed{9} \] 4. \(d - \frac{3}{4} = 11\) Add \(\frac{3}{4}\) to both sides: \[ d = 11 + \frac{3}{4} = \frac{44}{4} + \frac{3}{4} = \frac{47}{4} = \boxed{\frac{47}{4}}\] --- **• Correct Solution to the Equation \(3(x + 2) = 62\):** As previously calculated: \[ 3(x + 2) = 62 \] Divide both sides by 3: \[ x + 2 = \frac{62}{3}...