Solve for b2 in a = 1/2 h(b1+b2), if a = 16, h = 4, and b1 = 3. 16= 1/2* 4(3+b2) =6+2b2 or, b2= [16-6]/2= 5

Assuming you are referring to the area of a "trapezoid"; in which one calculates the Area, "A", as follows:

 A = 1/2* h(b1+b2) ;

in which: A = Area = 16 (given); 
               h = height = 4 (given);
               b1 = length of one of the two bases = 3 (given);
               b2 = length of the other of the two bases = ? (what we want to solve                                                                                            for) ;

Using the formula: A = 1/2 h(b1+b2) ;

Let us plug in our known values:

 →  16 = (1/2) * 4*(3 + b2) ;  → Solve for "b2".

 →Note: On the "right-hand side" on this equation: "(1/2)*(4) = 2 ." 

 So, we can rewrite the equation as:

 → 16 =   2*(3 + b2) ;  → Solve for "b2".

We can divide EACH side of the equation by "2"; to cancel the "2" on the "right-hand side" of the equation:

 → 16 / 2 =   [2*(3 + b2)] / 2  ;  → to get:

8 = (3 + b2) ;

 → Rewrite as: 8 = 3 + b2;

Subtract "3" from EACH side of the equation; to isolate "b2" on one side of the equation; and to solve for "b2" :

 → 8 - 3 = 3 + b2 - 3 ;  → to get:

b2 = 5;  From the 2 (TWO) answer choices given, this value,
"b2 = 5", corresponds with the following answer choice:

b2= [16-6]/2= 5 ; as this is the only answer choice that has: "b2 = 5".


As far getting "b2 = 5"  from: "b2= [16-6]/2= 5"; (as mentioned in the answer choice), we need simply to approach the problem in a slightly different manner.  Let us do so, as follows:

Start from: A = 1/2 h(b1+b2); and substitute our known (given) values):

→ 16 = (1/2) *4 (3 + b2) ; → Solve for "b2".

Note that: (½)*4 = 2;  so we can substitute "2" for: "(1/2) *4" ; 
and rewrite the equation as follows:

→ 16 = 2 (3 + b2) ;

Note: The distributive property of multiplication:

a*(b+c) = ab + ac ;

As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2). 

So we can substitute: "(6 + 2b2)" in lieu of "[2*(3 + b2)]"; and can rewrite the equation:

→ 16 = 6 + 2(b2) ; Now, we can subtract "6" from EACH side of the equation; to attempt to isolate "b2" on one side of the equation:

 → 16 - 6 =  6 + 2(b2) - 6 ;
      → Since "6-6 = 0"; the "6 - 6" on the "right-hand side" of the equation cancel.
→ We now have: 16 - 6 = 2*b2 ; 

Now divide EACH SIDE of the equation by "2"; to isolate "b2" on one side of the equation; and to solve for "b2":

   → (16 - 6) / 2 = (2*b2) / 2 ; 
     → (16 - 6) / 2 = b2 ;
       → (10) / 2 = b2 = 5.

NOTE: The other answer choice given: 

"16= 1/2* 4(3+b2)= 6+2b2" is incorrect; since it does not solve for "b2".