Question

Solve the equation. Check your answer.
7​(xminus​5)equals6​(xplus​5)

Answer 1

To solve the equation \( 7(x - 5) = 6(x + 5) \), follow these steps:

1. Distribute on both sides:
\[
7x - 35 = 6x + 30
\]

2. Move the \( 6x \) term from the right side to the left side by subtracting \( 6x \) from both sides:
\[
7x - 6x - 35 = 30
\]
This simplifies to:
\[
x - 35 = 30
\]

3. Now, add 35 to both sides to solve for \( x \):
\[
x = 30 + 35
\]
\[
x = 65
\]

Now we will check our answer by substituting \( x = 65 \) back into the original equation:

Original equation:
\[
7(x - 5) = 6(x + 5)
\]
Substituting \( x = 65 \):
\[
7(65 - 5) = 6(65 + 5)
\]
Calculating the left side:
\[
7(60) = 420
\]
Calculating the right side:
\[
6(70) = 420
\]

Since both sides equal, the solution \( x = 65 \) is correct.

Thus, the final answer is:
\[
\boxed{65}
\]