Answered

Experience the convenience of getting your questions answered at IDNLearn.com. Discover in-depth and trustworthy answers to all your questions from our experienced community members.

Your turn. Apply the definition of midpoint to solve this problem.

Point [tex]$M$[/tex] is the midpoint of line segment [tex]$AB$[/tex].

If [tex]$AM = 18$[/tex] and [tex]$MB = 2x - 5$[/tex], find the value of [tex]$x$[/tex].

A. 15
B. 11.5
C. 6.5
D. 46

Sagot :

GinnyAnsweridn
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
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.