Time scaling and shifting of delta function Learning signals and systems.
Solving time scaling and shifting problems.

For the  question 
$$x(t) = u(2t - 1)$$
First we shift by 1 to the right side and then we do time scaling , i.e divide by 2 on the time axis.

$x(t) = δ(2t - 1) $

Can we do the same thing for the above impulse function 

Is this the correct order of solving this:  


Shift to right by 1
time scale by half
change the area of the delta function by multiplying it to 1/2.
Note that the time-scaled and shifted Dirac delta impulse $\delta(2t-1)$ is non-zero where $2t-1=0$ is satisfied, i.e., at $t=\frac12$. It's area is indeed $\frac12$ because we have

$$\delta(at)=\frac{1}{|a|}\delta(t)\tag{1}$$

So for your example you get

$$\delta(2t-1)=\frac12\delta\left(t-\frac12\right)\tag{2}$$