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 for the next problem: 1. Six times a certain number decreased by two is four times the same number increased by twelve. Find the number. Step 1: Let the certain number be x. Translate the problem into an equation. "Six times a certain number decreased by two" can be written as 6x - 2. "Four times the same number increased by twelve" can be written as 4(x + 12). The problem states that these two expressions are equal. 6x - 2 = 4(x + 12) Step 2: Distribute the 4 on the right side of the equation. 6x - 2 = 4x + 48 Step 3: Gather the x terms on one side and the constant terms on the other side. Subtract 4x from both sides: 6x - 4x - 2 = 48 2x - 2 = 48 Add 2 to both sides: 2x = 48 + 2 2x = 50 Step 4: Solve for x by dividing both sides by 2. x = (50)/(2) x = 25 The number is 25. That's 2 down. 3 left today — send the next one.