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The given equation is:

\[
0.88x + 0.16(10 - x) = 0.40x
\]

Let's solve it step by step.

### Step 1: Distribute the \(0.16\) over \( (10 - x) \)
\[
0.88x + 0.16 \times 10 - 0.16 \times x = 0.40x
\]
\[
0.88x + 1.6 - 0.16x = 0.40x
\]

### Step 2: Combine like terms on the left-hand side
\[
(0.88x - 0.16x) + 1.6 = 0.40x
\]
\[
0.72x + 1.6 = 0.40x
\]

### Step 3: Move all the \(x\)-terms to one side
\[
0.72x - 0.40x = -1.6
\]
\[
0.32x = -1.6
\]

### Step 4: Solve for \(x\)
\[
x = \frac{-1.6}{0.32} = -5
\]

So, the solution to the equation is \(x = -5\).

Would you like further clarification on any of the steps?

### Related Questions:
1. How can we verify if the solution is correct by plugging it back into the original equation?
2. What happens if we solve a similar equation with different coefficients?
3. Can this type of equation have more than one solution?
4. How do equations like this appear in real-world applications?
5. What is the effect of distributing terms differently?

### Tip:
Always double-check your solution by substituting it back into the original equation to ensure correctness!

This detailed guide explains how to solve the linear equation 0.88x + 0.16(10 - x) = 0.40x step by step, including the use of the distributive property and combining like terms. The problem involves basic algebra concepts and is suitable for students in Grades 8-10.

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