$$ \frac{55}{100}\cdot560-\frac{25}{100}\cdot x=229.6 $$$$  $$

Let's solve the equation step by step:

The given equation is:

\[
\frac{55}{100} \cdot 560 - \frac{25}{100} \cdot x = 229.6
\]

### Step 1: Simplify the fractions
First, simplify the fractions $\frac{55}{100}$ and $\frac{25}{100}$:

\[
\frac{55}{100} = 0.55
\]
\[
\frac{25}{100} = 0.25
\]

Now, the equation becomes:

\[
0.55 \cdot 560 - 0.25 \cdot x = 229.6
\]

### Step 2: Multiply
Next, calculate $0.55 \cdot 560$:

\[
0.55 \cdot 560 = 308
\]

Now, the equation simplifies to:

\[
308 - 0.25x = 229.6
\]

### Step 3: Isolate the variable term
Subtract 308 from both sides of the equation:

\[
-0.25x = 229.6 - 308
\]

Simplify the right side:

\[
-0.25x = -78.4
\]

### Step 4: Solve for $x$
To isolate $x$, divide both sides by $-0.25$:

\[
x = \frac{-78.4}{-0.25} = 313.6
\]

### Final Answer:
\[
x = 313.6
\]

Would you like more details on any step, or do you have any other questions?

---

Here are some related questions:
1. How do you simplify fractions in equations?
2. What is the significance of isolating the variable in an equation?
3. Can you explain the steps to multiply decimals?
4. How do you handle negative signs when solving equations?
5. What happens if the coefficient of $x$ is positive instead of negative?
6. How would the solution change if the constant term were different?
7. Can you demonstrate solving a similar equation with different numbers?
8. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always double-check your arithmetic operations when dealing with decimals and fractions to avoid simple mistakes!

Learn how to solve the equation involving decimals and fractions: (55/100)*560 - (25/100)*x = 229.6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, decimals, and fractions. Suitable for students in Grades 7-9.

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