Final answer:
Upon simplifying the given equation -7g + 3 + 10g = 1 + 3g + 12, and combining like terms, we find that it simplifies to an untrue statement, 3 = 13. Therefore, the equation has no solutions.
Step-by-step explanation:
To solve the equation -7g + 3 + 10g = 1 + 3g + 12, we can start by simplifying both sides of the equation. We'll combine like terms on each side.
On the left side, we have -7g and +10g, which when combined gives us 3g. The equation now looks like this: 3g + 3 = 1 + 3g + 12.
Next, we can simplify the right side of the equation by combining the constant terms: 1 + 12, giving us 13. The equation simplifies to 3g + 3 = 3g + 13.
To find the value of g, we would normally isolate the variable on one side, but here we notice that 3g is present on both sides, and when we subtract 3g from both sides, we are left with 3 = 13.
This final statement is not true and indicates that there is no solution to this equation. No value of g can satisfy the equation, hence the equation has no solutions.
If we had obtained an identity such as 3 = 3, it would have meant that the equation has infinitely many solutions.