Higher November 2019 Paper 1 Q18
18 Solve \(\quad \dfrac{x + 15}{3} = 2(x + 10)\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(2x + 20\) | M1 | correct expansion |
| \(x + 15 = 6x + 60\) | M1dep | multiplication by 3 |
| \(15 - 60 = 6x - x\) or \(-45 = 5x\) or \(60 - 15 = x - 6x\) or \(45 = -5x\) | M1dep | collects terms |
| \(-9\) | A1 | SC2 \(-3\) from \(2x + 10\) or 1 from \(6x + 10\) |
| Alternative method 2 | ||
| \(2x + 20\) | M1 | correct expansion |
| \(\dfrac{x}{3} + 5 = 2x + 20\) and \(5 - 20 = 2x - \dfrac{x}{3}\) or \(-15 = \dfrac{5x}{3}\) or \(20 - 5 = \dfrac{x}{3} - 2x\) or \(15 = -\dfrac{5x}{3}\) | M1dep | splits the fraction and collects terms |
| \(15 - 60 = 6x - x\) or \(-45 = 5x\) or \(60 - 15 = x - 6x\) or \(45 = -5x\) | M1dep | multiplication by 3 |
| \(-9\) | A1 | SC2 \(-3\) from \(2x + 10\) or 1 from \(6x + 10\) |
| Alternative method 3 | ||
| \(6(x + 10)\) or \(6x + 60\) | M1 | multiplication of rhs by 3 |
| \(x + 15 = 6x + 60\) | M1dep | correct expansion |
| \(15 - 60 = 6x - x\) or \(-45 = 5x\) or \(60 - 15 = x - 6x\) or \(45 = -5x\) | M1dep | collects terms |
| \(-9\) | A1 | SC2 \(-3\) from \(2x + 10\) or 1 from \(6x + 10\) |