### Instruction: Solve $2z + i = iz + 3.$  Express your answer in the form $x + yi.$.### Response: I want to isolate $z$ on one side of the equation, so I will subtract $iz$ from both sides.
This gives me $2z - iz + i = 3.$
Now I want to factor out $z$ from the left side, so I can divide both sides by the coefficient of $z$.
This gives me $z(2 - i) = 3 - i.$
To divide both sides by $2 - i$, I need to multiply both sides by the conjugate of $2 - i$, which is $2 + i$, to get rid of the imaginary part in the denominator.
This gives me $z(2 - i)(2 + i) = (3 - i)(2 + i).$
I can simplify the left side by using the distributive property and the fact that $i^2 = -1.$
This gives me $z(4 - i^2) = (3 - i)(2 + i).$
Since $i^2 = -1$, the left side becomes $z(4 + 1) = z(5).$
The right side can also be simplified by using the distributive property and the fact that $i^2 = -1.$
This gives me $(3 - i)(2 + i) = 6 + 3i - 2i - i^2.$
Since $i^2 = -1$, the right side becomes $6 + 3i - 2i + 1 = 7 + i.$
So now I have $z(5) = 7 + i.$
To get $z$ by itself, I need to divide both sides by $5.$
This gives me $z = \frac{7 + i}{5}.$
To write $z$ in the form $x + yi$, I need to split the numerator into its real and imaginary parts.
This gives me $z = \frac{7}{5} + \frac{i}{5}.$