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 for the new equation. The equation is: (3)/(2)(2x-1) = (1)/(4)(5x-3) Step 1: Distribute the numbers on both sides of the equation. ((3)/(2) × 2x) - ((3)/(2) × 1) = ((1)/(4) × 5x) - ((1)/(4) × 3) 3x - (3)/(2) = (5x)/(4) - (3)/(4) Step 2: Eliminate the denominators by multiplying the entire equation by the least common multiple (LCM) of the denominators. The LCM of 2 and 4 is 4. Multiply every term by 4: 4(3x) - 4((3)/(2)) = 4((5x)/(4)) - 4((3)/(4)) 12x - 6 = 5x - 3 Step 3: Collect all terms with x on one side and constant terms on the other side. Subtract 5x from both sides: 12x - 5x - 6 = -3 7x - 6 = -3 Add 6 to both sides: 7x = -3 + 6 7x = 3 Step 4: Solve for x. Divide both sides by 7: x = (3)/(7) The final answer is (3)/(7). 3 done, 2 left today. You're making progress.