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]

Step a: AB plus BC equals AC

Justification: This is the definition of segment addition postulate.

Step b: 2x plus 6x plus 8 equals 32
Justification: This equation is obtained by substituting the lengths of AB and BC into the equation from step a.

Step c: 8x plus 8 equals 32
Justification: This equation is simplified using the distributive property by combining like terms on the left side of the equation.

Step d: 8x equals 24
Justification: This equation is obtained by subtracting 8 from both sides of the equation in step c.

Step e: x equals 3
Justification: This equation is obtained by dividing both sides of the equation in step d by 8.