This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution for question 3 from the image. 3. Solve (4r-3)/(6r+1) = (2r-1)/(3r+4) Step 1: Cross-multiply the terms. (4r-3)(3r+4) = (2r-1)(6r+1) Step 2: Expand both sides of the equation using the FOIL method. Left side: (4r)(3r) + (4r)(4) + (-3)(3r) + (-3)(4) 12r^2 + 16r - 9r - 12 12r^2 + 7r - 12 Right side: (2r)(6r) + (2r)(1) + (-1)(6r) + (-1)(1) 12r^2 + 2r - 6r - 1 12r^2 - 4r - 1 Step 3: Set the expanded expressions equal to each other. 12r^2 + 7r - 12 = 12r^2 - 4r - 1 Step 4: Move all terms to one side to solve for r. Subtract 12r^2 from both sides. 7r - 12 = -4r - 1 Step 5: Add 4r to both sides. 7r + 4r - 12 = -1 11r - 12 = -1 Step 6: Add 12 to both sides. 11r = -1 + 12 11r = 11 Step 7: Divide by 11. r = (11)/(11) r = 1 Step 8: Check for extraneous solutions (values of r that make the denominators zero). For 6r+1: 6(1)+1 = 7 ≠ 0 For 3r+4: 3(1)+4 = 7 ≠ 0 Since the denominators are not zero, r=1 is a valid solution. The final answer for 3 is r=1.