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 how to solve the equation: The given equation is: (2x)/(3) - 3 = (5)/(2)x + 6 Step 1: Gather all terms with x on one side and constant terms on the other side. Subtract (5)/(2)x from both sides: (2x)/(3) - (5)/(2)x - 3 = 6 Add 3 to both sides: (2x)/(3) - (5)/(2)x = 6 + 3 (2x)/(3) - (5x)/(2) = 9 Step 2: Find a common denominator for the fractions on the left side. The least common multiple (LCM) of 3 and 2 is 6. Rewrite the fractions with the common denominator: (2x · 2)/(3 · 2) - (5x · 3)/(2 · 3) = 9 (4x)/(6) - (15x)/(6) = 9 Step 3: Combine the fractions on the left side. (4x - 15x)/(6) = 9 (-11x)/(6) = 9 Step 4: Isolate x. Multiply both sides by 6: -11x = 9 · 6 -11x = 54 Divide both sides by -11: x = (54)/(-11) x = -(54)/(11) The final answer is -(54)/(11).