https://r2.erweima.ai/mathbot/image/1726410728417iztx9h08.jpg

The equation from the image is:

\[
15 - 5x = 5(3 - x)
\]

Let's solve this step by step:

1. **Distribute** the 5 on the right-hand side:
\[
5(3 - x) = 15 - 5x
\]

So the equation becomes:
\[
15 - 5x = 15 - 5x
\]

2. **Simplify**: Both sides of the equation are identical, meaning that for any value of \( x \), the equation will hold true. This is an example of an **identity**.

Thus, the solution is that **any real number** will satisfy this equation.

### Final Answer:
The solution is **all real numbers**, since the equation holds true for any \( x \).

Would you like further clarification on this process? Here are a few related questions:

1. What is the difference between an identity and a conditional equation?
2. How can we verify if an equation has no solution?
3. Can you show an example of an equation with one unique solution?
4. How do you solve an equation that has variables on both sides?
5. What happens if we get a contradiction instead of an identity?

**Tip**: Always double-check your work by substituting the solution back into the original equation to verify it holds true.

Learn how to solve the linear equation 15 - 5x = 5(3 - x) by using the distributive property and simplifying both sides. This equation is an identity, meaning it holds true for all real numbers. Suitable for students in Grades 8-10.

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