Answer: [C]: " 46 units ."
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Explanation:
The question (and corresponding image) asks:
" If B is the midpoint of AC, find the length of AC. "
Note:
The midpoint refers to the point in the middle of the line [segment].
In this particular question:
⇒ The line segment; AC is divided into 2 (two) equal segments of the same length:
AB = (x + 13) ; and:
BC = (2x + 3) ; {as per 'posted image'} ;
We are asked to find the length of AC.
[length of AB] + [length of BC] = [length of AC].
(x + 13) + (2x + 3) = [length of AC; for which we solve] :
We shall solving for x ; & then plug in the value to solve.
Note:
[length of AB] = [length of BC] ; Plug in our known values:
⇒ that is; (x + 13) = (2x + 3) ;
So, we have: " x + 13 = 2x + 3 "
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" x + 13 = 2x + 3 " ;
− x − 3 = − x − 3 " ;
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0 + 10 = x + 0 ;
→ " 10 = x " ;
↔ {Note: According to the "symmetric property" algebra:
"a = b " ; then " b = a"};
→ " x = 10 " ; {according to the "symmetric property of alm
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Another method:
When we have:
" x + 13 = 2x + 3 " ;
→ Subtract each side of the equation by x ; & subtract each side of the equation by 3 ;
to isolate x on one side of the equation —
[in this case, the 'right-hand' side of the equation];
and to solve for x ; as follows:
" x + 13 = 2x + 3 ";
Now; for each side of the question—on a separate 'left-hand' side; and: on a separate 'right-hand' side basis; we can combine the 'like terms' and simply:
For the left-hand side:
" x + 13 − x − 3 " : Combine the 'like terms":
+ x − x = 0 ; [that is: " +1x − 1x = 0"];
+ 13 − 3 = + 10 ; We have: " 0 + 10 = + 10 ".
Now, For the right-hand side:
" 2x + 3 − x − 3 " : Combine the 'like terms'; as follows:
" + 2x − x = x " ; {that is: " +2x − 1x = 1x = x "} ;
" + 3 − 3 " = 0 " . " x + 0 = x "
So: [left-hand side = right-hand side] ;
→ 10 = x ; ↔ " x = 10 ."
Both methods result in the same value for x ; that is: x = 10 ; which happens to suggest credibility.
Now, to find the length of AC ; which equals:
→ " x + 13 + 2x + 3 " ;
Then, we plug in our calculated value; 10 —for the values of x ;
and solve!
→ " 10 + 13 + (2*10) + 3 " = " 10 + 13 + 20 + 3 " = " 46 units ".
⇒ which corresponds to the correct answer: [C]: " 46 units."
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Hope this answer with explanation is helpful.
Best wishes!
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