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
Let the unknown number be x. Step 1: Translate the problem into an algebraic equation. "I'm thinking of a number." → x "When I multiply by 6" → 6x "add 8 to the result" → 6x + 8 "and multiply by (1)/(3) of the result" → (1)/(3)(6x+8) "I get -2." → = -2 So the equation is: (1)/(3)(6x+8) = -2 Step 2: Solve the equation for x. Multiply both sides of the equation by 3 to eliminate the fraction: 3 × (1)/(3)(6x+8) = -2 × 3 6x+8 = -6 Subtract 8 from both sides of the equation: 6x = -6 - 8 6x = -14 Divide both sides by 6: x = (-14)/(6) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2: x = -(7)/(3) The number is -(7)/(3). The final answer is -(7)/(3). That's 2 down. 3 left today — send the next one.