Bis the midpoint of ac. if ab= x +5 and bc = 2x-11, find the measure of ab.

Measurement of "AC" :

(x + 5) + (2x − 11) ;


Find the measurement of "AB" [which is: "(x+5)" ]: 

First, simplify to find the measurement of "AC" :

 (x + 5) + (2x − 11) ;

=  (x + 5) + 1(2x − 11) ;

=   x + 5 + 2x − 11 ;

 → Combine the "like terms" ; 

   x + 2x = 3x ;
   
   5 − 11 = - 6 ;

to get:  3x − 6 ; 

So,  (x + 5) + (2x − 11) =  3x − 6 ;

Solve for:  "(x + 5)"


We have: 


(x + 5) + (2x − 11) =  3x − 6  ;

Subtract:  "(2x − 11)" ;  from EACH SIDE of the equation ;
                                      to isolate "(x + 5)" on one side of the equation; 
                                      and to solve for "(x + 5)" ;

    →  (x + 5) + (2x − 11) − (2x − 11) =  (3x − 6) − (2x − 11) ;
  
         → (x + 5)  = (3x − 6) − (2x − 11) ;

  Note:  Simplify:  "(3x − 6) − (2x − 11)" ;

     →  (3x − 6) − (2x − 11)  ;
 
         =  (3x − 6) − 1(2x − 11) ;
 
         =   3x − 6 − 2x + 11 ;

   →  Combine the "like terms" :

         +3x − 2x = 1x = x ;
  
          -6 + 11 = 5 ; 

To get:  x + 5 ; 

So we have:

 x + 5 = x + 5 ; 


So, x = all real numbers.

x = ℝ