$r=\frac{x+y}{2}$

Make x the subject.

Multiply both sides of the equation by 2: 2 r = x + y .
Subtract y from both sides of the equation: 2 r − y = x .
Express x in terms of r and y : x = 2 r − y .
The final answer is: x = 2 r − y ​ .

Explanation

Understanding the Problem We are given the equation r = 2 x + y ​ and our goal is to isolate x and express it in terms of r and y . This means we want to rewrite the equation so that it starts with x = ...

Multiplying by 2 To isolate x , we first need to get rid of the fraction. We can do this by multiplying both sides of the equation by 2: 2 × r = 2 × 2 x + y ​ 2 r = x + y

Subtracting y Now, we need to isolate x on one side of the equation. To do this, we can subtract y from both sides: 2 r − y = x + y − y 2 r − y = x

Final Answer Therefore, we have successfully made x the subject of the formula. The equation is now: x = 2 r − y


Examples
In physics, this type of equation manipulation is often used when dealing with average velocities. For example, if r represents the average velocity of an object, x represents the final velocity, and y represents the initial velocity, then the equation r = 2 x + y ​ gives the average velocity in terms of the initial and final velocities. If you know the average velocity and the initial velocity, you can rearrange the equation to find the final velocity using x = 2 r − y .

Answered by GinnyAnswer | 2025-07-05

To isolate x in the equation r = 2 x + y ​ , we first multiply both sides by 2 to eliminate the fraction, resulting in 2 r = x + y . Then, we subtract y to isolate x , yielding the final result x = 2 r − y .
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Answered by Anonymous | 2025-07-19