Main Answer:
C) w = x - 3y3 , By isolating w in the equation x = 3(y + w) - 1 , the expression for \( w \) in terms of x and y is found to be x - 3y3, corresponding to option C. Understanding this process is crucial for solving equations and expressing variables in terms of others.
Therefore, the correct option is: C) w = (x - 3y) / 3.
Step-by-step explanation:
To find the value of w in terms of x and y in the equation x = 3(y + w) - 1 , first, isolate w by moving the other terms to the opposite side of the equation.
Begin by adding 1 to both sides: ( x + 1 = 3)(y + w). Next, divide both sides by 3 to solve for y + w: {x + 1}{3} = y + w . Finally, subtract y from both sides to obtain w in terms of x and y: w = {x - 3y3 , matching option C.
Understanding how to manipulate equations to express a variable in terms of others is fundamental in algebra. In this case, the steps involve basic arithmetic operations to isolate w and make it the subject of the equation. This skill is essential for solving a variety of mathematical problems and equations.
Therefore, the correct option is: C) w = (x - 3y) / 3.