B is the midpoint of AC. If Ab= x +5 and BC = 2x-11, find the measure of Ab.

1 answer:

4 0

__________________________

Measurement of "AC" :

(x + 5) + (2x <span>− 11) ;
________________________

Find the measurement of "AB" [which is: "(x+5)" ]:
______________________________________________
First, simplify to find the measurement of "AC" :
________________________________________
</span>(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 = <span>ℝ </span>

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