Final answer:
The correct answer is B) -2 and 7. In the equation 4x - 2(3x+7) = __x - __, these values result in no solution because they simplify to an impossible statement (0 = 7), showing a false condition that can never be satisfied.
Step-by-step explanation:
The student is asking which values in the equation 4x - 2(3x+7) = __x - __ will result in no solution. No solution occurs when you have a situation where after simplifying the equation, you end up with a statement that is always false, such as a non-zero constant equals zero (e.g. 0 = 7).
First, let's simplify the left side of the equation:
- Distribute the -2 across the parenthesis: 4x - 6x - 14.
- Combine like terms: -2x - 14.
Now, we have -2x - 14 = __x - __. For there to be no solution, the variable terms on both sides must cancel each other out while leaving inconsistent constants. This can only happen if the coefficients of x are the same on both sides, making it -2x on both sides, and the constants are different (implying that -14 is not equal to some other number). So, the values that result in no solution are -2 for the coefficient of x and any number different from -14 for the constant. Option C (-2 and 14) shows -2x - 14 = -2x - 14 which would simplify to 0 = 0, which always holds true, so that clearly has infinite solutions. Option B (-2 and 7) is the right choice because it represents -2x - 14 = -2x - 7 which simplifies to 0 = 7, an impossible equation, thus resulting in no solution.