Question

What is the value of x? Justify each step.

AC = 32

A horizontal line is labeled with three points, A, B, and C. Segment AB is labeled 2 x and segment BC is labeled 6 x plus 8. The diagram is not to scale.
The first column contains steps and the second column provides blanks where justification for each step should be written.The first column contains steps and the second column provides blanks where justification for each step should be written. The first column of row one says AB plus BC equals AC and the second column of row one has a blank after the letter a. The first column of row two says 2 x plus 6 x plus 8 equals 32 and the second column of row two has a blank after the letter b. The first column of row three says 8 x plus 8 equals 32 and the second column of row three has a blank after the letter c. The first column of row four says 8 x equals 24 and the second column of row four has a blank after the letter d. The first column of row five says x equals 3 and the second column of row five has a blank space after the letter e.
(5 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

AB + BC = AC (a)

2x + 6x + 8 = 32 (b)
8x + 8 = 32 (c)
8x = 24 (d)
x = 3 (e)

Justifications:
(a) By the segment addition postulate, the sum of the lengths of segment AB and segment BC equals the length of segment AC.
(b) By combining like terms, the sum of 2x and 6x plus 8 is equal to 32.
(c) By combining like terms again, the sum of 8x and 8 is equal to 32.
(d) By subtracting 8 from both sides of the equation, we can solve for 8x.
(e) By dividing both sides of the equation by 8, we can solve for x, giving us the value of x as 3.