Question

points p, q, and r are collinear. point q is between p and r, pq = 8x + 10, qr = 7x + 4, and pr = 20x - 1. find pr.

Explanation:

Step1: Use collinear - point property

Since P, Q, R are collinear and Q is between P and R, then $PQ + QR=PR$. Substitute the given expressions: $(8x + 10)+(7x + 4)=20x-1$.

Step2: Simplify the left - hand side

Combine like terms: $8x+7x + 10 + 4=15x + 14$. So, $15x+14 = 20x-1$.

Step3: Solve for x

Subtract 15x from both sides: $15x-15x + 14=20x-15x-1$, which gives $14 = 5x-1$. Add 1 to both sides: $14 + 1=5x-1 + 1$, so $15 = 5x$. Divide both sides by 5: $x=\frac{15}{5}=3$.

Step4: Find PR

Substitute $x = 3$ into the expression for PR: $PR=20x-1=20\times3-1=60 - 1=59$.

Answer:

59