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: Write down the inequality. (1)/(3)(2x+5) + (3)/(2)(x-1) 3(x+1) Step 2: Multiply both sides of the inequality by the least common multiple (LCM) of the denominators (3 and 2), which is 6, to eliminate the fractions. 6 ( (1)/(3)(2x+5) + (3)/(2)(x-1) ) 6 ( 3(x+1) ) 2(2x+5) + 9(x-1) 18(x+1) Step 3: Distribute the numbers into the parentheses on both sides. (2 × 2x) + (2 × 5) + (9 × x) + (9 × -1) (18 × x) + (18 × 1) 4x + 10 + 9x - 9 18x + 18 Step 4: Combine like terms on the left side of the inequality. (4x + 9x) + (10 - 9) 18x + 18 13x + 1 18x + 18 Step 5: Move all terms containing x to one side and constant terms to the other side. Subtract 13x from both sides. 1 18x - 13x + 18 1 5x + 18 Step 6: Subtract 18 from both sides. 1 - 18 5x -17 5x Step 7: Divide both sides by 5 to solve for x. (-17)/(5) x This can also be written as: x -(17)/(5) The final answer is x -(17)/(5).