Question

Solve the equation for the given variable.

B=((r+z)/(2))m for r

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for r, we can isolate it by multiplying both sides of the equation by 2/B:

2/B * B = 2/B * ((r+z)/2)m

2 = (r+z)m

Then, divide both sides by m:

2/m = (r+z)

Finally, subtract z from both sides of the equation to solve for r:

r = (2/m) - z

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation for r, we need to isolate the variable r on one side of the equation.

Step 1: Multiply both sides of the equation by 2 to remove the fraction:
2B = (r + z) * m

Step 2: Distribute the m to both terms in the parentheses:
2B = r * m + z * m

Step 3: Subtract z * m from both sides of the equation:
2B - z * m = r * m

Step 4: Divide both sides of the equation by m:
(r * m) = (2B - z * m) / m

Step 5: Simplify the equation:
r = (2B - z * m) / m

Therefore, the solution for r is r = (2B - z * m) / m.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation B=((r+z)/(2))m for the variable r, we need to isolate the variable r on one side of the equation. Here's how you can do it step by step:

1. Start with the given equation: B = ((r + z) / 2) * m

2. Multiply both sides of the equation by 2 to eliminate the denominator: 2B = (r + z) * m

3. Distribute the m on the right side of the equation: 2B = rm + zm

4. Subtract zm from both sides of the equation: 2B - zm = rm

5. Now, we can rearrange the equation by swapping the sides: rm = 2B - zm

6. Finally, divide both sides of the equation by m to solve for r: r = (2B - zm) / m

Therefore, the solution for r in terms of B, z, and m is r = (2B - zm) / m.