Intermediate November 2023 Unit 1 Q19
19. Solve the equation \(\dfrac{10x + 2}{3} - \dfrac{7x - 3}{5} = 9\). [4]
| Scheme | Marks | Comments |
|---|---|---|
| Correct equation e.g. \(\dfrac{50x + 10 - 21x + 9}{(15)} = \dfrac{9 \times 3 \times 5}{(15)}\) | B2 | FT until 2nd error. Award B1 for one of the following:
|
| (\(29x + 19 = 135\)) \(29x = 116\) | B1 | |
| \(x = 4\) | B1 | Mark final answer. Award the final B0 for \(\dfrac{116}{29}\). If FT leads to a whole number answer, it must be shown as a whole number. Otherwise, accept a fraction. Allow B2B1B1 for a correct embedded answer BUT only B2B1B0 if contradicted by \(x \ne 4\) or equivalent. Note 1: \(\dfrac{50x + 10 - 21x - 9}{(15)} = \dfrac{135}{(15)}\) B1 (one error –9) \(29x = 134\) B1 \(x = \dfrac{134}{29}\) B1 Note 2: \(\dfrac{50x + 10 - 21x + 9}{(15)} = \dfrac{9}{(15)}\) B1 (one error =9) \(29x = -10\) B1 \(x = \dfrac{-10}{29}\) B1 Note 3: \(\dfrac{50x + 10 - 21x - 9}{(15)} = \dfrac{9}{(15)}\) B0 B0 B0 (2 errors –9 & 9) Award B2B1B1 for unsupported answer of 4, or for an answer which has come from a non-algebraic method. |