Final answer:
After solving the equation 7x + 12 = 51 - 8x by simplifying and solving for x, it is determined that there is one solution (x = 2.6).
Step-by-step explanation:
The equation given is 7x + 12 = 51 - 8x. To find out how many solutions there are to this equation, you need to solve for x. Start by simplifying and rearranging terms to isolate the variable on one side of the equation.
- Add 8x to both sides of the equation: 7x + 8x + 12 = 51
- Combine like terms: 15x + 12 = 51
- Subtract 12 from both sides: 15x = 39
- Divide by 15: x = 39 / 15
- Simplify the answer: x = 2.6
Since we've found a single value for x, the equation has one solution.