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 the solution to the problem: The problem states: "18 is decreased by the sum of a number and 2. The result is 9 less than 3 times the number. Find the number." Step 1: Let the unknown number be x. "The sum of a number and 2" can be written as (x + 2). "18 is decreased by the sum of a number and 2" translates to 18 - (x + 2). This is the left side of our equation. Step 2: Formulate the right side of the equation. "3 times the number" is 3x. "9 less than 3 times the number" means 3x - 9. This is the right side of our equation. Step 3: Set up the full equation. 18 - (x + 2) = 3x - 9 Step 4: Simplify the left side of the equation. 18 - x - 2 = 3x - 9 16 - x = 3x - 9 Step 5: Gather x terms on one side and constant terms on the other. Add x to both sides and add 9 to both sides. 16 + 9 = 3x + x 25 = 4x Step 6: Solve for x by dividing both sides by 4. x = (25)/(4) x = 6.25 The number is 6.25. Drop the next question.