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+7-(8x)/(3) = (17)/(6) - (5x)/(2), we need to find a common denominator for all fractions. Step 1: Identify the denominators. The denominators are 1 (for x and 7), 3, 6, and 2. The least common multiple (LCM) of 1, 3, 6, and 2 is 6. Step 2: Multiply every term in the equation by the LCM (6) to eliminate the denominators. 6(x) + 6(7) - 6((8x)/(3)) = 6((17)/(6)) - 6((5x)/(2)) Step 3: Simplify each term. 6x + 42 - (2 × 8x) = 17 - (3 × 5x) 6x + 42 - 16x = 17 - 15x Step 4: Combine like terms on each side of the equation. On the left side: 6x - 16x = -10x So, the equation becomes: -10x + 42 = 17 - 15x Step 5: Move all terms containing x to one side and all constant terms to the other side. Add 15x to both sides: -10x + 15x + 42 = 17 5x + 42 = 17 Subtract 42 from both sides: 5x = 17 - 42 5x = -25 Step 6: Solve for x. Divide both sides by 5: x = (-25)/(5) x = -5 The final answer is -5.