Final answer:
The correct expression to replace the question mark in the equation 162 - 16 = 4(?) is 36.5, which when multiplied by 4 yields 146, the same as 162 - 16. None of the options provided (42 - 4, 42 - 16, 2x - 2) yield the correct result to make the original equation true for all values of x.
Step-by-step explanation:
The student is asking which expression can replace the question mark in the equation 162 - 16 = 4(?) so that the equation is true for all values of x. To solve this, we need to find an expression that when multiplied by 4, yields 162 - 16.
Let's consider the given options:
- A) 42 - 4: If we multiply this by 4, we get 4(42) - 4(4) = 168 - 16, which is not equal to 162 - 16.
- B) 42 - 16: If we multiply this by 4, we get 4(42) - 4(16) = 168 - 64, which again is not equal to 162 - 16.
- C) 2x - 2: If we multiply this by 4, we get 4(2x - 2) = 8x - 8. Since no specific value for x is given, we cannot determine a specific numerical value for the left side.
However, none of the expressions given lead to a solution that makes the original equation true for all values of x. Since the equation is meant to be true for all values of x, there must be a constant result after the expression in the parentheses is multiplied by 4. We can find the correct expression by simplifying the left side of the original equation:
162 - 16 = 146
To find the correct expression to replace the question mark, divide 146 by 4:
146 / 4 = 36.5
Therefore, the correct expression to replace the question mark is 36.5, which is not listed among the options given.