As per the given problem, we have
A, B, and C are collinear points and B is between A and C.
Also , we are given that
[tex] AB=5,BC=3x+7,AC=5x-2 [/tex]
As the point B is between A and C, so only possibility is the point will be the mid point of AC, unless ratio of division is not given.
So we can write
[tex] AC=AB+BC\\
\\
\text{Substitute the values we get}\\
\\
5x-2=5+3x+7\\
\\
\text{take the like terms together we get}\\
\\
5x-3x=2+5+7\\
\\
2x=14\\
\\
\text{Divide both the sides by 2 we get}\\
\\
x=7\\ [/tex]
Answer:
The value of x is 7.
Step-by-step explanation:
Given,
A, B, and C are col-linear points and B is between A and C,
⇒ AC = AB + BC
We have, AB = 5, BC=3x+7, AC=5x−2
By substituting the value,
[tex]5x - 2 = 5 + 3x + 7[/tex]
[tex]5x - 2 = 3x + 12[/tex]
[tex]5x - 3x = 12 + 2[/tex]
[tex]2x = 14[/tex]
⇒ [tex]x = 7[/tex]
Hence, the value of x is 7.
