The only equation that correctly balances both sides and sets the sum equal to a given value is 3x + 5 + 10x - 7 = 180.
The image shows three equations:
3x + 5 = 10x - 7: This equation is missing a term on the right side to balance the equation.
3x + 5 + 10x - 7 = 180: This equation adds the missing term (10x) to the right side and sets the sum equal to 180. This is a valid equation to solve for x.
3x + 5 + 10x - 7 = 90: This equation is similar to the second equation, but it sets the sum equal to 90 instead of 180. This is not a valid equation to solve for x in the context of the problem.
Therefore, the only equation that correctly balances both sides and sets the sum equal to a given value is 3x + 5 + 10x - 7 = 180.