Final answer:
To solve for the missing value in the equation 3y + 2x = x + 4, we perform algebraic operations to isolate y, resulting in the equation y = - (1/3)x + (4/3). Thus, the missing value in the solution is (b) (1/3). So, the best answer is b, (1/3)
Step-by-step explanation:
To complete the missing value in the solution to the equation 3y + 2x = x + 4, let's isolate y by performing some algebraic manipulations:
Subtract x from both sides of the equation: 3y + 2x - x = 4.
Simplify the equation: 3y + x = 4.
Subtract x from both sides of the equation: 3y = 4 - x.
Finally, divide both sides of the equation by 3 to solve for y: y = (4 - x) / 3.
We want the terms to match choices a) through d), which are given in terms of fractions with x as the numerator. This leads us to express y as:
y = - (1/3)x + (4/3)
Comparing the coefficients of x to the given options, we find that the correct answer is (b) (1/3).
So, the best answer is b, (1/3).