To determine which equation has no solutions, let's analyze each one:
-
\(6x + 4 = 6x + 4\)
This is an identity. Both sides are always equal for any value of \(x\). Therefore, it has infinite solutions. -
\(-6x + 4 = 6x + 3\)
We can solve for \(x\): \[ -6x - 6x = 3 - 4 \ -12x = -1 \ x = \frac{1}{12} \] This equation has one solution. -
\(6x + 3 = -6x + 3\)
Solving for \(x\): \[ 6x + 6x = 3 - 3 \ 12x = 0 \ x = 0 \] This equation has one solution. -
\(-6x + 4 = -6x + 3\)
Here, we move the terms around: \[ -6x + 6x = 3 - 4 \ 0 = -1 \] This statement is false, meaning there are no values of \(x\) that will satisfy this equation. Therefore, it has no solutions.
The equation with no solutions is:
\(\mathbf{-6x + 4 = -6x + 3}\)