Question

question
point q is on line segment \\( \overline{pr} \\). given \\( qr = 3x \\), \\( pq = x + 6 \\), and \\( pr = 5x - 4 \\), determine the numerical length of \\( pq \\).
answer
attempt 1 out of 4
\\( pq = \\)

Explanation:

Step1: Apply segment addition postulate

$PQ + QR = PR$

Step2: Substitute given expressions

$(x+6) + 3x = 5x - 4$

Step3: Simplify left side

$4x + 6 = 5x - 4$

Step4: Solve for $x$

$6 + 4 = 5x - 4x \implies x = 10$

Step5: Calculate length of $\overline{PQ}$

$PQ = x + 6 = 10 + 6$

Answer:

16