7(x−3)−2(x−8)= 15− 2(x+5)

To solve the equation \( 7(x - 3) - 2(x - 8) = 15 - 2(x + 5) \), we will first expand and then simplify both sides.

1. Expand the left side:

\[ 7(x - 3) - 2(x - 8) = 7x - 21 - 2x + 16 \]

Combine like terms:

\[ (7x - 2x) + (-21 + 16) = 5x - 5 \]

2. Expand the right side:

\[ 15 - 2(x + 5) = 15 - 2x - 10 \]

Combine like terms:

\[ 15 - 10 - 2x = 5 - 2x \]

3. Set the two sides equal:

\[ 5x - 5 = 5 - 2x \]

4. Add \(2x\) to both sides to isolate \(x\):

\[ 5x + 2x - 5 = 5 \]

This simplifies to:

\[ 7x - 5 = 5 \]

5. Add \(5\) to both sides:

\[ 7x = 10 \]

6. Divide by \(7\):

\[ x = \frac{10}{7} \]

Therefore, the solution to the equation is:

\[ \boxed{\frac{10}{7}} \]