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 solve the equation (x)/(2) - (1)/(5) = (x)/(3) + (1)/(4), we need to find a common denominator for all fractions. Step 1: Identify the denominators. The denominators are 2, 5, 3, and 4. The least common multiple (LCM) of 2, 5, 3, and 4 is 60. Step 2: Multiply every term in the equation by the LCM (60) to eliminate the denominators. 60((x)/(2)) - 60((1)/(5)) = 60((x)/(3)) + 60((1)/(4)) Step 3: Simplify each term. 30x - 12 = 20x + 15 Step 4: Move all terms containing x to one side and all constant terms to the other side. Subtract 20x from both sides: 30x - 20x - 12 = 15 10x - 12 = 15 Add 12 to both sides: 10x = 15 + 12 10x = 27 Step 5: Solve for x. Divide both sides by 10: x = (27)/(10) The final answer is (27)/(10).