Question

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Part 1
Solve the equation. Check your answer.
11​(xminus​5)equals10​(xplus​5)
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Part 1
xequals
  
enter your response here
​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation \( 11(x - 5) = 10(x + 5) \), follow these steps:

1. Distribute both sides:

\[
11x - 55 = 10x + 50
\]

2. Rearrange the equation by getting all terms involving \( x \) on one side and constant terms on the other side:

\[
11x - 10x = 50 + 55
\]

3. Simplify both sides:

\[
x = 105
\]

So, the solution is:

\[
x = 105
\]

### Checking the answer:

Substitute \( x = 105 \) back into the original equation:

Left side:
\[
11(105 - 5) = 11(100) = 1100
\]

Right side:
\[
10(105 + 5) = 10(110) = 1100
\]

Both sides are equal, so the solution \( x = 105 \) is correct.

Final answer:

\[
\boxed{105}
\]