Let's solve the given problem step by step.
Given that [tex]\( M \)[/tex] is the midpoint of line segment [tex]\( AB \)[/tex], we know that [tex]\( AM = MB \)[/tex].
We are provided with the following information:
1. [tex]\( AM = 18 \)[/tex]
2. [tex]\( MB = 2x - 5 \)[/tex]
Since [tex]\( AM \)[/tex] and [tex]\( MB \)[/tex] are equal (because [tex]\( M \)[/tex] is the midpoint), we can set up the equation:
[tex]\[
AM = MB
\][/tex]
Substituting the given values, we get:
[tex]\[
18 = 2x - 5
\][/tex]
Now, we solve for [tex]\( x \)[/tex].
1. Add 5 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
18 + 5 = 2x - 5 + 5
\][/tex]
[tex]\[
23 = 2x
\][/tex]
2. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{23}{2}
\][/tex]
[tex]\[
x = 11.5
\][/tex]
So the value of [tex]\( x \)[/tex] is 11.5.
To determine the correct multiple-choice option, we compare our answer to the choices given:
- a. 15
- b. 11.5
- c. 6.5
- d. 46
Our solution corresponds to option b. Therefore, the correct answer is [tex]\( \boxed{b} \)[/tex].
