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 to eliminate the denominators. (4r-3)(3r+4) = (2r-1)(6r+1) Step 2: Expand both sides of the equation. Left side: 12r^2 + 16r - 9r - 12 = 12r^2 + 7r - 12 Right side: 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: 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 validity (denominators not equal to zero). For r=1: 6r+1 = 6(1)+1 = 7 ≠ 0 3r+4 = 3(1)+4 = 7 ≠ 0 The solution is valid. The final answer is r=1.