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 question 46: Step 1: Distribute the -2 into the parentheses. 5 - 2(3x - 1) = -13 5 - (2 × 3x) - (2 × -1) = -13 5 - 6x + 2 = -13 Step 2: Combine the constant terms on the left side of the equation. (5 + 2) - 6x = -13 7 - 6x = -13 Step 3: Subtract 7 from both sides of the equation to isolate the term with x. 7 - 6x - 7 = -13 - 7 -6x = -20 Step 4: Divide both sides by -6 to solve for x. (-6x)/(-6) = (-20)/(-6) x = (20)/(6) x = (10)/(3) The solution to the equation is x = (10)/(3). Comparing this to the given options: (A) 3 (B) 4 (C) -1 (D) -3 It seems there might be a discrepancy between my calculated answer and the provided options, as (10)/(3) is not among them. Let me re-check the calculation. Re-checking Step 1: 5 - 2(3x - 1) = -13 5 - 6x + 2 = -13 (Correct) Re-checking Step 2: 7 - 6x = -13 (Correct) Re-checking Step 3: -6x = -13 - 7 -6x = -20 (Correct) Re-checking Step 4: x = (-20)/(-6) x = (10)/(3) (Correct) Since the calculated answer (10)/(3) is not among the options (A) 3, (B) 4, (C) -1, (D) -3, there might be an error in the question's options or the question itself. However, if I were forced to choose the closest integer, none are particularly close. Let's assume there might be a typo in the question or options. If the right side was, for example, -19: 7 - 6x = -19 -6x = -26 x = 26/6 = 13/3 If the right side was -11: 7 - 6x = -11 -6x = -18 x = 3 (Option A) Let's assume the question intended for x=3 to be the answer and work backward to see what the right side of the equation would be. If x=3: 5 - 2(3(3) - 1) 5 - 2(9 - 1) 5 - 2(8) 5 - 16 = -11 So, if the equation was 5 - 2(3x - 1) = -11, then x=3 would be the correct answer. Given the options, and the common practice in multiple-choice questions to have one correct answer, it's highly probable that the intended answer was x=3, and the right side of the equation was meant to be -11 instead of -13. However, based on the exact question provided: 5 - 2(3x - 1) = -13 The correct solution is x = (10)/(3). Since this is not an option, I cannot select one of the given choices. If I must choose the closest integer option, (10)/(3) ≈ 3.33. Option (A) is 3. Given the constraint to select from the given options, and assuming a slight error in the problem statement or options, I will proceed with the assumption that x=3 was the intended answer, which would mean the equation should have been 5 - 2(3x - 1) = -11. If we strictly follow the given equation, none of the options are correct. However, if we consider the possibility of a typo in the constant on the right side, and that x=3 is an option, it's the most plausible intended answer. Let's re-evaluate if there's any other interpretation. No, the steps are straightforward. I will state the calculated answer and then address the options. The final answer is x = (10)/(3). Based on the provided options, none of them match the calculated value of x = (10)/(3). There might be an error in the question or the options. If the equation were 5 - 2(3x - 1) = -11, then x=3 would be the correct answer, which is option (A). That's 2 down. 3 left today — send the next one.