To solve the equation \( U + ka = ba \) for \( a \), follow these steps:

### Step 1: Isolate the term with \( a \)
Subtract \( U \) from both sides to isolate the terms involving \( a \):
\[
ka = ba - U
\]

### Step 2: Solve for \( a \)
Now, divide both sides of the equation by \( k \) to solve for \( a \):
\[
a = \frac{ba - U}{k}
\]

This is the solution for \( a \) in terms of \( U \), \( k \), and \( b \).

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Would you like further details on these steps, or have any questions?

Here are some related questions:

1. How does this formula change if \( b = 1 \)?
2. What happens when \( k = 0 \)?
3. How can this equation be applied to real-world problems?
4. Can you solve for other variables in the equation?
5. What is the physical interpretation of this equation in mechanics?

**Tip**: Always check for conditions where division might not be possible, like \( k = 0 \), to avoid undefined results.

Learn how to solve the linear equation U + ka = ba for a with step-by-step instructions. This problem explores core algebraic concepts such as isolating variables and solving for a. Suitable for students in Grades 9-10.

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