Answered

Find expert answers and community-driven knowledge on IDNLearn.com. Get step-by-step guidance for all your technical questions from our dedicated community members.

Find the value of [tex]$x$[/tex] if [tex]$A, B$[/tex], and [tex][tex]$C$[/tex][/tex] are collinear points and [tex]$B$[/tex] is between [tex]$A$[/tex] and [tex][tex]$C$[/tex][/tex].

[tex]AB = 5x - 1, BC = 14, AC = 25 - x[/tex]

A. 2
B. 6
C. 5
D. 9

Sagot :

GinnyAnsweridn
To solve for [tex]\( x \)[/tex] given the collinear points [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] where [tex]\( B \)[/tex] is between [tex]\( A \)[/tex] and [tex]\( C \)[/tex], we can use a property of collinear points: the sum of segments [tex]\( AB \)[/tex] and [tex]\( BC \)[/tex] should equal the segment [tex]\( AC \)[/tex].

Given:
- [tex]\( AB = 5x - 1 \)[/tex]
- [tex]\( BC = 14 \)[/tex]
- [tex]\( AC = 25 - x \)[/tex]

We can write the equation:
[tex]\[ AB + BC = AC \][/tex]
Substituting the given lengths:
[tex]\[ (5x - 1) + 14 = 25 - x \][/tex]

Next, combine the constant terms on the left side:
[tex]\[ 5x - 1 + 14 = 25 - x \][/tex]
[tex]\[ 5x + 13 = 25 - x \][/tex]

Now, move the [tex]\( x \)[/tex] terms to one side of the equation and the constants to the other side to isolate [tex]\( x \)[/tex]:
[tex]\[ 5x + x = 25 - 13 \][/tex]
[tex]\[ 6x = 12 \][/tex]

Divide both sides by 6:
[tex]\[ x = 2 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{2} \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.