Question

Which equation has no solution
-6x + 4 = -6x + 3
6x + 4 = 6x + 4
6x + 3 = -6x + 3
-6x + 4 = 6x + 3

Answer 1

To determine which of the given equations has no solution, we can solve each one:

1. **Equation 1**: \(-6x + 4 = -6x + 3\)

Rearranging gives:
\(-6x + 6x + 4 = 3\)
or
\(4 = 3\)

This is False. Therefore, this equation has no solution.

2. **Equation 2**: \(6x + 4 = 6x + 4\)

This simplifies to \(0 = 0\), which is always true. Therefore, this equation has infinitely many solutions.

3. **Equation 3**: \(6x + 3 = -6x + 3\)

Rearranging gives:
\(6x + 6x = 3 - 3\)
or
\(12x = 0\)

This means \(x = 0\). Therefore, this equation has one solution.

4. **Equation 4**: \(-6x + 4 = 6x + 3\)

Rearranging gives:
\(-6x - 6x = 3 - 4\)
or
\(-12x = -1\)

This means \(x = \frac{1}{12}\). Therefore, this equation has one solution.

Based on the above evaluations, the equation that has no solution is:

\(-6x + 4 = -6x + 3\)