12x – 3x + 11 > 4x – (17 – 9x)
a. x> -14/11
b. x< -14/11
c. x< 7
d. x> -7

The answer is: [C]: x < 7 .

Explanation:

Given:

12x – 3x + 11 > 4x – (17 – 9x) ;

We need to simplify EACH side of the inequality; and then rewrite:

Let us start with the "left-hand side" :

12x – 3x + 11

We see that among the three terms, there are 2 (two) "like terms"; 
  "12x" and "-3x" ;

So, 12x – 3x = 9x ; and bring down the remaining term, " +11" ;

9x + 11 ;

Now, let us simplify the 'right-hand side' of the inequality:

4x  – (17 – 9x) ;

Treat this expression as:

 4x – 1(17 – 9x) ;  

(Note: The coefficient "1" is implied; since anything multiplied by "1" is that  same value").

Note the "distributive property of multiplication" :

 a* (b + c) = ab + ac ; AND:
 a* (b – c) = ab – ac ;

So, we have the expression:

  4x – 1(17 – 9x) ;

Take the:  -1*(17 – 9x); and simplify;

-1*(17 – 9x) =  (-1 * 17) – (-1 * 9x) = -17 – (-9x) = -17 + 9x ;

We have:

-17 + 9x ; Rewrite as: 9x – 17

Now, bring down the "4x"; and rewrite the expression:

9x – 17 + 4x ;

Notice that there are 2 (two) "like terms" out of the 3 (three) terms in this expression:

+9x and +4x ;  

Combine these like terms; and simplify: 

4x + 9x = 13x ; 

Now, bring down the "– 17 " ; and rewrite the entire "right-hand side" expression: 

13x – 17 ;

Now, we can rewrite the entire equality, by substituting our simplified expressions:

9x + 11 > 13x – 17 ; Now, solve for "x" ;

Subtract "9x" from EACH side; and add "17" to EACH side;

9x + 11 – 9x + 17 > 13x – 17 – 9x + 17 ;

28 > 4x ;  

Now, divide EACH side of the inequality by "4", to isolate "x" on one side of the inequality; and to solve for "x" ;

 28 / 4 >  4x / 4 ;

   7 > x ; or, write as: x < 7 ; which is: "Answer choice: [C] ".