Final answer:
To simplify the expression 6y-2=-2(4-x), you distribute the -2, combine like terms, and solve for y, resulting in y = (1/3)x - 1.
Step-by-step explanation:
The student is asking for help with simplifying the algebraic expression 6y-2=-2(4-x). To simplify this expression, first distribute the -2 across the terms inside the parentheses: -2 times 4 and -2 times -x. This gives us 6y - 2 = -8 + 2x. Adding 2 to both sides we get 6y = 2x - 6.
Next, if we want to express y in terms of x, we divide both sides by 6, which gives us y = (1/3)x - 1. This expresses y as a function of x in a simplified form, which is the answer the student is looking for.