Question

Which equation has infinitely many solutions.
2x=1-2x

Answer 1

To determine if the equation \(2x = 1 - 2x\) has infinitely many solutions, we can solve it.

1. Start with the given equation:
\[
2x = 1 - 2x
\]

2. Add \(2x\) to both sides to combine like terms:
\[
2x + 2x = 1
\]
which simplifies to:
\[
4x = 1
\]

3. Now, divide both sides by 4 to solve for \(x\):
\[
x = \frac{1}{4}
\]

This equation has exactly one solution, \(x = \frac{1}{4}\). Therefore, it does **not** have infinitely many solutions.

An equation will have infinitely many solutions if it simplifies to a true statement like \(0 = 0\), which is not the case here.

In conclusion, the equation \(2x = 1 - 2x\) has a unique solution, not infinitely many.