Final answer:
Expanding and simplifying the equation 3(4−2x)=6(−x+2) results in an identity, which is true for all values of x. Thus, there are an infinite number of solutions to this equation.
Step-by-step explanation:
To determine how many solutions the equation 3(4−2x)=6(−x+2) has, we need to first expand the equation and simplify it.
Expanding both sides:
Now we have a simplified equation:
12 - 6x = -6x + 12
If we try to solve for x, we subtract 12 from both sides, and we end up with:
-6x = -6x
This equation is true for all values of x, meaning we have an infinite number of solutions. This occurs because the equation is an identity, where both sides are always equal regardless of the value of x.