Question

AB = 8x + 3, BC =2x + 7 and AC = 80 Find value of AB and BC

Answer 1

Answers:
 1)  The value of AB  is:  " 59 units."
 2) The value of BC  is: "21 units."
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 3) The value of AB  +  BC ;

     =   59  units  +   21  units ;

     =   [the value of AC ] ;

     =  {" 80 units ".}.
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Step-by-step explanation:                                            

Given the following—and based on the assumption that we are dealing with:  "geometric lines"—and/or: "geometric line segments"—we are asked to:  
  "Find the value of:  " AB and BC" .
    {Given: " AB = (8x + 3) ;  BC  = (2x + 7) ;  AC = 80 ".}.
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Note:  The following "line graphs" are "Not Drawn to Scale."

           

        |    (8x + 3)     |      (2x + 7)       |

        |<--------------->|<------------------->|

<----·|----------------->|<------------------->|  {Note:  "Not drawn to scale."}.
       A                   B                         C
<-----|----------------->|<------------------->|

       A                                               C

<-----|<--------------------------------------->|  

<-----|----------------------------------------->|          

       A             {"AC = 80 ".}             C

         

 <---|------------------------------------------>|
       A       {"AC = 80 ".}.                  C

       |  (8x + 3) ;   +       (2x + 7)      =  80 ;  

<-----|----------------->|<--------------------->I
       A                    B                         C

So:  We have to find the value of:
     1) AB ; which is: (8x + 3) ;  And:
     2) BC ;  which is:  (2x + 7) .

To get these values; we need to find the value for "x".

So:   (8x + 3)  +  (2x + 7)   = 80  ;  
      ➝  8x + 3 + 2x + 7 = 80 ;

      ➝ Now, Let us combine the "like terms" on the "left-hand side" of the equation:
    +8x + 2x + 3 + 7  ;

      ➝  to get: + 8x + 2x = + 10x  ; and:
                       +3 + 7 = 10 ;

      To get:  "10x + 10" ;

Now, we can rewrite the equation:
       {" 70 ÷ 10 = 7 ."}.   " 10x + 10 = 80 ;

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To solve for "x" ; there are many ways:
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Method 1)  We have:  " 10x + 10 = 80 " ;
 ➝ Now, subtract "10" from each side of the question;
       10x + 10 − 10 = 80 − 10 ;
to get:  10x = 70 ;

 ➝  Now, divide each side of the equation by: "10" ; to isolate "x" on one side of the equation;  & to solve for "x" ;

  10x /10 = 70 /10 ;   to get:  " x = 7 "

Method 2)
 At the moment above in which we have:
" 10x = 70 " ;   we know that "10x ÷ 10 = 1x" ; and then "70 ÷ 10 = 7 ".

       {Note that any value; divided by "10" ;  is equal to:
{"that value" moved Back by:  "One" decimal space.}.  

So:  " 1x = 7 " ; ↔ " x = 7 ".

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Method 3) :

When we have:  " 10x /10 = 70 /10 " ;  we have " 1x " on the "left-hand side" of the equation;  and:  "{ 70 /10 }" = {" 70 ÷ 10 = 7 ."}.

Note that: {" 70 ÷ 10 = 7 "} ; can be determined in many ways;
    For instance: {" 70 ÷ 10 = ? "} ;  

 ➝  The zeros for Both the numerator and denominator "cancel out"—

and we have:  " $\frac{70}{10}$ " ;  
 ➝  Cancel out each of the two (2) "zeros" ; and we have:  " $\frac{7}{1} = 7.$ "

 ➝  This is assuming that we figure out that:  " $\frac{10x}{10}=1x =x$ ."

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Now; let's find the correct values for this Brainly Question:
1) AB  =  8x + 3 ;  
Substitute our calculated value for "x" ; and solve:

➝  AB = 8x + 3 ;  ↔  8(7)  + 3   =  56  + 3  = 59 .

➝ BC  = 2x + 7 ;  ↔ 2(7)  +  7   =  14 + 7   =  21 .
Note:
➝  AC  =  80 = AB  + BC   ≟   59 + 21  ≟  80 ?  Yes!

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Answers:
 1) The value of AB  is:  " 59 units."
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 2) The value of BC  is:   "21 units."
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 3) The value of AB + BC  ;

           = 59 units + 21 units  =  {The value of AC }  =  "80 units".}.

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Hope this answer—along with explanations—is helpful to you.

  Best wishes in your academic pursuits!

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