Let's solve the equation:

\[
10 + 10(x + 3) = -x - 10(-x + 1)
\]

### Step 1: Distribute the numbers outside the parentheses.
\[
10 + 10x + 30 = -x + 10x - 10
\]

### Step 2: Combine like terms on both sides.
On the left side:
\[
10 + 30 + 10x = 40 + 10x
\]

On the right side:
\[
-x + 10x - 10 = 9x - 10
\]

So, the equation becomes:
\[
40 + 10x = 9x - 10
\]

### Step 3: Isolate the variable \(x\) by subtracting \(9x\) from both sides.
\[
40 + x = -10
\]

### Step 4: Subtract 40 from both sides to solve for \(x\).
\[
x = -50
\]

So, the solution is \(x = -50\).

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the solution change if the right side of the equation were different, e.g., \(-x - 10(-x - 1)\)?
2. What is the role of distributing in solving this equation?
3. How can you verify that the solution \(x = -50\) is correct?
4. What if the equation had more terms involving \(x\)? How would that change the approach?
5. Can you think of a real-life situation where you would need to solve an equation like this?

**Tip:** Always simplify both sides of the equation as much as possible before solving for the variable.

Learn how to solve a linear equation involving distributive property and combining like terms step-by-step. This problem covers basic algebraic concepts, suitable for students in Grades 7-9.

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