Answer
a) $x=x+2$
b) $2(x+1)=2x+2$
Work Step by Step
$a)$ Example of a linear equation with no solution:
$$x=x+2$$
When solving:
$$x-x=2$$
$$0=2$$
It has no solution since $0$ does not equal to $2$.
$b)$ Example of a linear equation with infinitely many solutions:
$$2(x+1)=2x+2$$
When solving:
$$2x+2=2x+2$$
$$2x-2x-=2-2$$
$$0=0$$
It has infinitely many solutions since we got an identity: $0$ equals to $0$ and it does not depend on the variable $x$.
