Final answer:
After simplifying the equation 4x + 2(x - 5) = 3(2x - 4), we find that the variable terms cancel each other out, resulting in an untrue statement, indicating that there is no solution to the equation.
Step-by-step explanation:
To find out how many solutions the equation 4x + 2(x - 5) = 3(2x - 4) has, let's simplify and solve it step by step:
- Distribute the terms inside the parentheses: 4x + 2x - 10 = 6x - 12.
- Combine like terms: 6x - 10 = 6x - 12.
- Try to isolate x, but notice that the x terms cancel each other out: 6x - 6x = -10 + 12.
- This leaves us with 0 = 2, which is not true, therefore there is no solution to the equation.
Typically, a linear equation like the one we started with will have one solution, unless a situation like this arises where equivalent terms on both sides lead to a false statement.