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
To determine the value of t in the given equation, we will first find a common denominator to clear the fractions. The equation is: (1)/(7) + (2t)/(3) = (15t - 3)/(21) + 1 Step 1: Find the least common multiple (LCM) of the denominators 7, 3, and 21. The LCM of 7, 3, and 21 is 21. Step 2: Multiply every term in the equation by the LCM (21) to eliminate the denominators. 21 ( (1)/(7) ) + 21 ( (2t)/(3) ) = 21 ( (15t - 3)/(21) ) + 21 (1) Step 3: Simplify each term. (21)/(7) + (42t)/(3) = (15t - 3) + 21 3 + 14t = 15t - 3 + 21 Step 4: Combine the constant terms on the right side of the equation. 3 + 14t = 15t + 18 Step 5: Isolate the terms with t on one side and the constant terms on the other side. Subtract 14t from both sides: 3 = 15t - 14t + 18 3 = t + 18 Subtract 18 from both sides: 3 - 18 = t -15 = t The value of t is: -15