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's the solution to the problem: The problem is to solve the equation: (3)/(t-2) = (4)/(3t+4) Step 1: Cross-multiply to eliminate the denominators. 3(3t+4) = 4(t-2) Step 2: Distribute the numbers into the parentheses. 3 × 3t + 3 × 4 = 4 × t - 4 × 2 9t + 12 = 4t - 8 Step 3: Rearrange the equation to gather terms with t on one side and constant terms on the other. Subtract 4t from both sides. 9t - 4t + 12 = -8 Subtract 12 from both sides. 5t = -8 - 12 Step 4: Combine like terms. 5t = -20 Step 5: Solve for t by dividing both sides by 5. t = (-20)/(5) t = -4 The solution is t = -4.