Select the correct answer.
Given the following formula, solve for $y$.
$w=\frac{x-y}{2}-z$
A. $\quad y=2(w+z)-x$
B. $y=x-(2 w+z)$
C. $y=x-2(w+z)$
D. $y=2 w+z-x$
Answer (1)
Add z to both sides: w + z = 2 x − y .
Multiply both sides by 2: 2 ( w + z ) = x − y .
Isolate y : y = x − 2 ( w + z ) .
The correct answer is y = x − 2 ( w + z ) .
Explanation
Understanding the Problem We are given the equation w = 2 x − y − z and asked to solve for y . This involves isolating y on one side of the equation using algebraic manipulations.
Isolating the term with y First, we want to isolate the term containing y . We can add z to both sides of the equation: w + z = 2 x − y
Removing the fraction Next, we multiply both sides of the equation by 2 to get rid of the fraction: 2 ( w + z ) = x − y
Isolating y Now, we want to isolate y . We can add y to both sides and subtract 2 ( w + z ) from both sides: y = x − 2 ( w + z )
Final Answer Comparing our result with the given options, we see that it matches option C. Therefore, the correct answer is y = x − 2 ( w + z ) .
Examples
In physics, you might have a formula that relates force, mass, and acceleration, but you need to rearrange it to solve for mass. Similarly, in economics, you might rearrange an equation to solve for a specific variable like price or quantity. This skill is essential for making predictions and understanding relationships between different quantities in various fields.
