Given rectangle pqrs with pq=qr, pq=sp, and sq=5√2. find rq. a) not enough info. b) √2. c) 5. d) 5√2

PQRS is a square. By definition of a square, it has 4 equal sides, in this case segments PQ, QR, RS and PS. Based on the given, all segments are equal as proof that PQRS is a square. Furthermore, this square has a units per segment. Thus, all 4 segments measure a units. 
SQ is the adjacent side, which cuts the square in triangles. 
a^2+a^2=(5√2)^2 hence, a=5 units. C is the correct answer.

You get all of the 'x's on one side of the equation, and everything else
on the other side.

I'll use your equation to demonstrate.  Please watch closely:

                                                 6x = 5x + 7

Subtract  5x  from each side:        x  = 7 .

Oops.  Ran out of steps.  That's all this one needs.

' 7 ' is the 'solution' to this equation.  That means:  ' 7 ' is the number
that  'x'  must be in order for the equation to be a true statement. 
If  'x'  is any other number but 7, the equation makes a statement
that's false.

Example:  What if we make  'x'  ten ?  Then the equation says

                6 (10)  =  5 (10) + 7

                  60     =   50    + 7

                     60  =  57      HONK !   Not true !    'x' can only be ' 7 ' .