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 distribute and simplify both sides of the equation.

1. Distribute \( 7 \) and \( -2 \) on the left side: \[ 7(x - 3) = 7x - 21 \] \[ -2(x - 8) = -2x + 16 \] So, the left side becomes: \[ 7x - 21 - 2x + 16 = (7x - 2x) + (-21 + 16) = 5x - 5 \]

2. Now, distribute \( -2 \) on the right side: \[ -2(x + 5) = -2x - 10 \] So, the right side becomes: \[ 15 - 2x - 10 = 5 - 2x \]

3. Now we have: \[ 5x - 5 = 5 - 2x \]

4. To isolate \( x \), we can add \( 2x \) to both sides: \[ 5x + 2x - 5 = 5 \] \[ 7x - 5 = 5 \]

5. Next, add \( 5 \) to both sides: \[ 7x = 10 \]

6. Finally, divide both sides by \( 7 \) to solve for \( x \): \[ x = \frac{10}{7} = \frac{10}{7} \]

Thus, the solution is: \[ x = \frac{10}{7} \]