Sure, let's solve this problem step by step, applying the definition of the midpoint.
Given that point [tex]\( M \)[/tex] is the midpoint of line segment [tex]\( AB \)[/tex], it means that the segment is divided into two equal parts by [tex]\( M \)[/tex]. Therefore, [tex]\( AM = MB \)[/tex].
We have the following values:
- [tex]\( AM = 18 \)[/tex]
- [tex]\( MB = 2x - 5 \)[/tex]
Since [tex]\( AM \)[/tex] and [tex]\( MB \)[/tex] are equal parts of the segment [tex]\( AB \)[/tex]:
[tex]\[ AM = MB \][/tex]
So,
[tex]\[ 18 = 2x - 5 \][/tex]
Now we need to solve this equation for [tex]\( x \)[/tex]:
1. Start by isolating [tex]\( x \)[/tex]. First, add 5 to both sides of the equation:
[tex]\[ 18 + 5 = 2x - 5 + 5 \][/tex]
[tex]\[ 23 = 2x \][/tex]
2. Now, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{23}{2} = \frac{2x}{2} \][/tex]
[tex]\[ x = 11.5 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 11.5 \)[/tex].
Therefore, the correct answer is:
b. 11.5
