Answer:
[tex] x = 3 [/tex]
Step-by-step explanation:
From the figure given, we have points A,B, and C, that are collinear. Therefore, according to the segment addition postulate, [tex] AB + BC = AC [/tex].
We are given that:
AB = 9x + 7
BC = -5x + 20
AC = 39
An equation that can be used to solve for x would be:
[tex] (9x + 7) + (-5x + 20) = 39 [/tex]
Solve for x
[tex] 9x + 7 - 5x + 20 = 39 [/tex]
[tex] 9x - 5x + 7 + 20 = 39 [/tex]
[tex] 4x + 27 = 39 [/tex]
Subtract 27 from both sides
[tex] 4x + 27 -27 = 39 - 27 [/tex]
[tex] 4x = 12 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{12}{4} [/tex]
[tex] x = 3 [/tex]
