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: Step 1: Write the given equation. (1+4x)/(2) - (5+2x)/(7) = x-2 Step 2: Find a common denominator for the fractions on the left side. The least common multiple of 2 and 7 is 14. (7(1+4x))/(14) - (2(5+2x))/(14) = x-2 Step 3: Combine the fractions on the left side. (7(1+4x) - 2(5+2x))/(14) = x-2 Step 4: Distribute the numbers in the numerator. (7 + 28x - 10 - 4x)/(14) = x-2 Step 5: Combine like terms in the numerator. (24x - 3)/(14) = x-2 Step 6: Multiply both sides by 14 to eliminate the denominator. 24x - 3 = 14(x-2) Step 7: Distribute 14 on the right side. 24x - 3 = 14x - 28 Step 8: Move all terms with x to one side and constant terms to the other side. Subtract 14x from both sides. 24x - 14x - 3 = -28 10x - 3 = -28 Step 9: Add 3 to both sides. 10x = -28 + 3 10x = -25 Step 10: Divide by 10 to solve for x. x = (-25)/(10) x = -(5)/(2) The final answer is -(5)/(2).