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
Step 1: Distribute the fraction on the left side of the equation. 5x - (2)/(3)(x-4) = -3 - (3)/(2)x 5x - (2)/(3)x + (2)/(3) × 4 = -3 - (3)/(2)x 5x - (2)/(3)x + (8)/(3) = -3 - (3)/(2)x Step 2: Clear the denominators by multiplying the entire equation by the least common multiple (LCM) of 3 and 2, which is 6. 6 ( 5x - (2)/(3)x + (8)/(3) ) = 6 ( -3 - (3)/(2)x ) 6(5x) - 6((2)/(3)x) + 6((8)/(3)) = 6(-3) - 6((3)/(2)x) 30x - 4x + 16 = -18 - 9x Step 3: Combine like terms on each side of the equation. (30-4)x + 16 = -18 - 9x 26x + 16 = -18 - 9x Step 4: Move all terms containing x to one side and constant terms to the other side. Add 9x to both sides: 26x + 9x + 16 = -18 35x + 16 = -18 Subtract 16 from both sides: 35x = -18 - 16 35x = -34 Step 5: Solve for x. x = -(34)/(35) The final answer is -(34)/(35). Send me the next one 📸