Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

If [tex]\( P, Q \)[/tex], and [tex]\( R \)[/tex] are any three collinear points such that [tex]\( Q \)[/tex] lies between [tex]\( P \)[/tex] and [tex]\( R \)[/tex], find the value of [tex]\( x \)[/tex] if [tex]\( PR = 5x \)[/tex], [tex]\( PQ = 10 \)[/tex], and [tex]\( QR = 3x - 2 \)[/tex].

A. 1
B. 8
C. 6
D. 4

Sagot :

GinnyAnswer
To solve for [tex]\( x \)[/tex] given the collinear points [tex]\( P \)[/tex], [tex]\( Q \)[/tex], and [tex]\( R \)[/tex] with [tex]\( Q \)[/tex] lying between [tex]\( P \)[/tex] and [tex]\( R \)[/tex], we start with the given distances:

[tex]\[ PR = 5x \][/tex]
[tex]\[ PQ = 10 \][/tex]
[tex]\[ QR = 3x - 2 \][/tex]

Since [tex]\( Q \)[/tex] lies between [tex]\( P \)[/tex] and [tex]\( R \)[/tex], the distance [tex]\( PR \)[/tex] can be expressed as the sum of the distances [tex]\( PQ \)[/tex] and [tex]\( QR \)[/tex]:

[tex]\[ PR = PQ + QR \][/tex]

Substituting the given distances into the equation:

[tex]\[ 5x = 10 + (3x - 2) \][/tex]

First, simplify the right-hand side of the equation:

[tex]\[ 5x = 10 + 3x - 2 \][/tex]
[tex]\[ 5x = 3x + 8 \][/tex]

Next, isolate [tex]\( x \)[/tex] by subtracting [tex]\( 3x \)[/tex] from both sides:

[tex]\[ 5x - 3x = 8 \][/tex]
[tex]\[ 2x = 8 \][/tex]

To find the value of [tex]\( x \)[/tex], divide both sides by 2:

[tex]\[ x = \frac{8}{2} \][/tex]
[tex]\[ x = 4 \][/tex]

Thus, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{4} \)[/tex].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.