To determine which equation has no solution, let's analyze each of the options you've provided.
A: \[ 3 = 5x + 4 \] Rearranging gives: \[ 5x = 3 - 4 \implies 5x = -1 \implies x = -\frac{1}{5} \] This has a solution.
B: \[ 10 = 4 + 2x \] Rearranging gives: \[ 10 - 4 = 2x \implies 6 = 2x \implies x = 3 \] This has a solution.
C: \[ 2 = 2x - 10 \] Rearranging gives: \[ 2 + 10 = 2x \implies 12 = 2x \implies x = 6 \] This has a solution.
D: \[ = 5x + 6 \] This appears to be incomplete as it lacks an equation (for example, a left-hand side) for us to analyze. Assuming it translates into something like \(0 = 5x + 6\), we'd find: \[ 5x = -6 \implies x = -\frac{6}{5} \] This would also have a solution, if structured that way.
However, if we look for an equation with no solutions, an example would be an equation that simplifies to a false statement, like \(0 = 5\).
Since we do not have one in the options provided based on the checks, option D in its current representation appears incomplete and may potentially be the one with "no solutions" due to its lack of definition.
To truly find the answer, please ensure that the equations are presented completely. If we treat D as any form of nonsensical equality, it might be the correct answer. Otherwise, based on the current choices, none have been defined properly to yield no solution unless D is improperly formed as noted.