Question

is x=x+3 an inconsistent equation? why or why not?

Answer 1

Are there any values for `x` that satisfy the given equation ?

Answer 2

inconsistent equation (roughly) means that there are no x-solutions that satisdy both of the statements.
When you say, x=x+3, that is just like saying

y=x+3
y=x

you can see though, that no matter what you plug for x into the equations, their y solutions won't ever be same.

lets just take a look at the graphs,
https://www.desmos.com/calculator/sn2fm04xmt

See? they don't intersect,
and in order for a system of equations to have a solution yo have to have two of the graphs intersect with weach other.