Fred's current age is (x-1) years. i) What was he 4 years ago? ii) What will he be 8 years from now? iii) How old is he now, if his age in 8 years time will be three times his age 4 years ago?

Here are the solutions to the problems. 4. a) Fred's current age is (x-1) years. i) Was he 4 years ago? Step 1: Subtract 4 from his current age. (x-1) - 4 = x-5 Fred's age 4 years ago was (x-5) years. ii) Will he be 8 years from now? Step 1: Add 8 to his current age. (x-1) + 8 = x+7 Fred's age 8 years from now will be (x+7) years. iii) Is he now, if his age in 8 years time will be three times his age 4 years ago? Step 1: Set up the equation based on the given information. x+7 = 3(x-5) Step 2: Distribute the 3 on the right side. x+7 = 3x-15 Step 3: Subtract x from both sides. 7 = 2x-15 Step 4: Add 15 to both sides. 22 = 2x Step 5: Divide by 2. x = 11 Step 6: Calculate Fred's current age (x-1). Current age = 11-1 = 10 Fred's current age is 10 years. b) The perimeter of a rectangular cocoa farm is 497 km. The length of the farm is 2(1)/(2) times the width. Let W be the width and L be the length. Given L = 2(1)/(2)W = (5)/(2)W. The perimeter P = 2(L+W). i) Find the width. Step 1: Substitute the given values into the perimeter formula. 497 = 2((5)/(2)W + W) Step 2: Combine the terms inside the parenthesis. 497 = 2((5)/(2)W + (2)/(2)W) 497 = 2((7)/(2)W) Step 3: Simplify the right side. 497 = 7W Step 4: Divide by 7 to find W. W = (497)/(7) W = 71 The width of the farm is 71 km. ii) Find the length of the farm. Step 1: Use the relationship L = (5)/(2)W. L = (5)/(2) × 71 L = (355)/(2) L = 177.5 The length of the farm is 177.5 km. 5. a) Factorize: (x-y)(3m+n) - (x-y)(m-2n). Step 1: Identify the common factor, which is (x-y). Step 2: Factor out the common term. (x-y)[(3m+n) - (m-2n)] Step 3: Simplify the expression inside the square brackets. (x-y)[3m+n - m+2n] (x-y)[(3m-m) + (n+2n)] (x-y)(2m+3n) The factored expression is (x-y)(2m+3n). b) Given p = 2-3x \\ 5-2y , q = -1 \\ 5 , and p-q = 6 \\ 8 . Find the value of (x+y). Step 1: Use the equation p-q = 6 \\ 8 to find p. p = q + 6 \\ 8 p = -1 \\ 5 + 6 \\ 8 p = -1+6 \\ 5+8 p = 5 \\ 13 Step 2: Equate this result with the given expression for p. 2-3x \\ 5-2y = 5 \\ 13 Step 3: Form two separate equations from the components. Equation 1: 2-3x = 5 Equation 2: 5-2y = 13 Step 4: Solve Equation 1 for x. -3x = 5-2 -3x = 3 x = (3)/(-3) x = -1 Step 5: Solve Equation 2 for y. -2y = 13-5 -2y = 8 y = (8)/(-2) y = -4 Step 6: Find the value of (x+y). x+y = -1 + (-4) x+y = -5 The value of (x+y) is -5. c) i) Find the truth set of (x-1)/(2) (1)/(2) + x. Step 1: Multiply the entire inequality by 2 to eliminate denominators. 2 × ((x-1)/(2)) 2 × ((1)/(2)) + 2 × (x) x-1 1 + 2x Step 2: Subtract x from both sides. -1 1 + x Step 3: Subtract 1 from both sides. -1-1 x -2 x The truth set is x x -2 . ii) Illustrate the answer in (i) on the number line. Step 1: Draw a number line. Step 2: Mark -2 on the number line. Step 3: Draw a closed circle at -2 (because x is greater than or equal to -2). Step 4: Draw an arrow extending to the right from -2, indicating all values greater than -2. cccccccc <--- & & -------------------------------------> \\ & -2 & & & & & & x 6. a) Copy and complete the table for the relation y = 5-2x for -3 x 4. Step 1: Calculate y for each given x value using the equation y = 5-2x. For x=-3: y = 5-2(-3) = 5+6 = 11 For x=-2: y = 5-2(-2) = 5+4 = 9 For x=-1: y = 5-2(-1) = 5+2 = 7 For x=0: y = 5-2(0) = 5-0 = 5 For x=1: y = 5-2(1) = 5-2 = 3 For x=2: y = 5-2(2) = 5-4 = 1 For x=3: y = 5-2(3) = 5-6 = -1 For x=4: y = 5-2(4) = 5-8 = -3 The completed table is: |c|c|c|c|c|c|c|c|c| x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & 11 & 9 & 7 & 5 & 3 & 1 & -1 & -3 \\ b) Using a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes ox and oy for -5 x 5 and -12 y 12. Step 1: Draw the x-axis and y-axis on a graph sheet. Step 2: Label the x-axis from -5 to 5, with 2 cm representing 1 unit. Step 3: Label the y-axis from -12 to 12, with 2 cm representing 2 units. c) i) Using the table, plot all the points of the relation y=5-2x. Step 1: Plot the points from the completed table: (-3, 11), (-2, 9), (-1, 7), (0, 5), (1, 3), (2, 1), (3, -1), (4, -3) on the graph drawn in 6(b). ii) Draw a straight line through all the points. Step 1: Connect the plotted points with a straight line. d) Using the graph, find the: (Since I cannot draw a graph, I will calculate these values using the equation y=5-2x.) i) value of y when x=-2.6. Step 1: Substitute x=-2.6 into the equation y=5-2x. y = 5 - 2(-2.6) y = 5 + 5.2 y = 10.2 The value of y when x=-2.6 is 10.2. ii) value of x when y=-2.8. Step 1: Substitute y=-2.8 into the equation y=5-2x. -2.8 = 5 - 2x Step 2: Subtract 5 from both sides. -2.8 - 5 = -2x -7.8 = -2x Step 3: Divide by -2. x = (-7.8)/(-2) x = 3.9 The value of x when y=-2.8 is 3.9. iii) gradient of the line. Step 1: The equation of the line is y = 5-2x. This is in the form y = mx+c, where m is the gradient. Step 2: Identify the coefficient of x. The gradient of the line is -2. That's 2 down. 3 left today — send the next one.