To determine which equation has no solution, let’s first simplify the expression you provided:
We have:
4x + 2 = 6 – 2x + 9 + 3x – 6 – 2x + 8
Combining like terms on the right side, we get:
- Constant terms: 6 – 6 + 9 + 8 = 17
- Variable terms: -2x + 3x – 2x = -x
So we can rewrite the equation as:
4x + 2 = -x + 17
Next, let’s move all terms involving x to one side and constant terms to the other. Adding x to both sides:
4x + x + 2 = 17
5x + 2 = 17
Now, subtracting 2 from both sides gives:
5x = 15
Finally, dividing both sides by 5:
x = 3
This means that the original equation has a solution. Therefore, to find equations with no solution, we need to look for contradictory statements, such as:
0 = 5
This kind of equation suggests that there is no value for x that can satisfy the equation. Unfortunately, based on the original equation given, we do not have such a case. Upon inspection, if the original input led to a contradiction during simplification, that would indicate no solution exists but in this case it does have a valid solution.