Question

Solve the equation. Check your answer.
12​(xminus​5)equals11​(xplus​5)
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Part 1
xequals
  
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​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation \( 12(x - 5) = 11(x + 5) \), we will first distribute the constants on both sides:

1. Distribute on the left side:
\[
12(x - 5) = 12x - 60
\]

2. Distribute on the right side:
\[
11(x + 5) = 11x + 55
\]

Now we rewrite the equation:
\[
12x - 60 = 11x + 55
\]

Next, we will isolate \( x \). We can do this by moving \( 11x \) to the left side and \( -60 \) to the right side:
\[
12x - 11x = 55 + 60
\]
This simplifies to:
\[
x = 115
\]

Now, we have our solution:
\[
x = 115
\]

### Check the answer:
Substituting \( x = 115 \) back into the original equation to verify:

1. Calculate the left side:
\[
12(115 - 5) = 12(110) = 1320
\]

2. Calculate the right side:
\[
11(115 + 5) = 11(120) = 1320
\]

Both sides are equal, confirming that our solution is correct. Thus, the solution is:
\[
\boxed{115}
\]