Final answer:
To make the expression 5/4x + 6 equivalent to 1/2x + 6, we need to subtract 3/4x from 5/4x. Subtracting 3/4x results in the coefficient of x becoming 1/2, which is the coefficient desired in the target expression.
Step-by-step explanation:
The question asks which additional operation should be included in the expression 5/4x + 6 to make it equivalent to 1/2x + 6. To find the required operation, we can align the coefficients of x in both expressions. Since the coefficient of x in the desired expression is 1/2, and the coefficient in the given expression is 5/4, we need to subtract something from 5/4 to get 1/2.
Starting with 5/4x + 6, we subtract an unknown quantity 'a' to get the target expression: (5/4 - a)x + 6 = 1/2x + 6.
Solving for 'a', we have: 5/4 - a = 1/2. Thus, 'a' = 5/4 - 1/2.
Finding a common denominator, we get: 'a' = (5/2) / 2 - 1/2 = (5 - 2) / 4 = 3/4. Therefore, the operation needed is subtraction of 3/4x, which matches option Ch -3x/4.