You should use algebra in all parts of this question, showing your working clearly. (a) Solve the following equations, giving your answers as integers or as fractions in their simplest form. (i) 12x + 4=50 - 11x [2] (ii) 4 -=(6x - 3) = 3 + 3x [3] (b) Simplify the following expression: 4-22 x2 - 4x + 4 [3] (c) Solve the following equation by completing the square: x2 + 14x - 51 = 0. [3] (d) A student was asked to rearrange the formula: 6a = 2d - 5(6 - 2) to make d the subject (assuming that 12 + c / 0). The student's incorrect attempt is shown below. ba = 2d - 416-d Clear the fractions By multiplying By 6 36a= 12d-3c(36-2d) Multiply out the Bracket 36a =12d-108c-2d Collect the d terms 36a +108c = 10d Divide By 10 to Give d= 36a + 108c (i) Write out a correct rearrangement of the formula. [3] (ii) Identify and explain, as if directly to the student, two of the mistakes they have made. [2]