https://file.aiquickdraw.com/mathbot/file/1728611332994no2x8cqa.jpg

The equation in the image is:

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

Let's solve it step by step:

### Step 1: Expand both sides.
Expand the terms with parentheses:

\[
10 + 10(x + 3) = 10 + 10x + 30 = 10x + 40
\]

On the right side:

\[
-x - 10(-x + 1) = -x + 10x - 10 = 9x - 10
\]

So the equation becomes:

\[
10x + 40 = 9x - 10
\]

### Step 2: Collect like terms.
Move all the terms involving \(x\) to one side and constant terms to the other side:

\[
10x - 9x = -10 - 40
\]

Simplify:

\[
x = -50
\]

### Final solution:
The solution to the equation is:

\[
x = -50
\]

Would you like more details on any part of the solution or have any questions?

Here are some related questions you might find useful:
1. What if the equation had more complex terms?
2. How can I verify my solution for linear equations?
3. What is the general approach to solving linear equations with parentheses?
4. How does distributing work in more complex polynomial equations?
5. Can this equation be solved graphically?

**Tip**: Always expand the terms inside parentheses first to avoid mistakes when simplifying an equation.

Learn how to solve the linear equation 10 + 10(x + 3) = -x - 10(-x + 1) with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property and the equality theorem. Suitable for students in Grades 8-10.

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