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

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

➝ This is assuming that we figure out that: " [tex]\frac{10x}{10}=1x =x[/tex] ."

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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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