Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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 hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.