Question

What is the value of w?

Answer 1

If you have a no solution choice that will be your answer because w+34=w-22 
you would subtract w from both sides to get 34=-22 and that's not true therefore it would be a no solution equation.

Answer 2

we have

$\frac{(w+3)}{4} =\frac{(w-2)}{2}$

Solve for w

$\frac{(w+3)}{4} =\frac{(w-2)}{2}\\2(w+3)=4(w-2) \\2w+6=4w-8 \\4w-2w=6+8 \\2w=14 \\w=14/2 \\w=7$

therefore

the answer is the option A

$w=7$