Final answer:
The false statement is b) A solution to 2 = 2x + 4 is 8 because the solution to this equation is actually x = -1.
Step-by-step explanation:
The task at hand is to identify the false statement among the given options and to provide a reasoning for the selection. Let's evaluate each statement to see which one is not true.
- a) A solution to 8 = -x + 10 is 2. To determine the truth of this statement, solve for x: x = 10 - 8, which gives us x = 2. This statement is true.
- b) A solution to 2 = 2x + 4 is 8. Solve for x using algebra: Subtract 4 from both sides to get -2 = 2x, then divide by 2 to get x = -1. The statement is false because x is not 8, but -1.
- c) A solution to -x + 10 = 2x + 4 is 8. Combine like terms by adding x to both sides and subtracting 4 from both sides to obtain 3x = 6, which simplifies to x = 2. Hence, this statement is also false.
- d) There are no values of x and y that make y = -x + 10 and y = 2x + 4 true at the same time. This is a system of equations. To solve, set the two equations equal: -x + 10 = 2x + 4, leading to 3x = 6, which gives x = 2. Substitute x into either equation to find y; y = 8. There is a solution (x, y) = (2, 8), making the statement false.
From the given options, the false statement is b) A solution to 2 = 2x + 4 is 8 because upon solving the equation correctly, the solution is x = -1, not 8.