Question

q is the midpoint of \\(\overline{pr}\\). if \\(qr = 2x\\) and \\(pr = 3x + 2\\), what is \\(qr\\)? diagram: segment \\(pr\\) with midpoint \\(q\\), \\(qr\\) labeled \\(2x\\), \\(pr\\) labeled \\(3x + 2\\) simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since Q is the midpoint of \( \overline{PR} \), \( PR = 2 \times QR \). So we have the equation \( 3x + 2 = 2\times(2x) \).

Step2: Solve for x

Simplify the right side: \( 3x + 2 = 4x \). Subtract \( 3x \) from both sides: \( 2 = 4x - 3x \), so \( x = 2 \).

Step3: Find QR

We know \( QR = 2x \), substitute \( x = 2 \): \( QR = 2\times2 = 4 \).

Answer:

4