Question

if j - k - p, and if jp = 4x - 10, kp = 2x + 5, and jk = 31, then find jp. after you enter your answer press go. jp =

Explanation:

Step1: Use the segment - addition postulate

Since \(J - K - P\), we know that \(JP=JK + KP\).
Substitute the given expressions: \(4x-10=31+(2x + 5)\).

Step2: Simplify the right - hand side of the equation

Simplify \(31+(2x + 5)\) to \(2x+36\). So the equation becomes \(4x-10=2x + 36\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x-10=2x-2x + 36\), which gives \(2x-10=36\).
Add \(10\) to both sides: \(2x-10 + 10=36+10\), so \(2x=46\).
Divide both sides by \(2\): \(x = 23\).

Step4: Find \(JP\)

Substitute \(x = 23\) into the formula for \(JP\). Since \(JP=4x-10\), then \(JP=4\times23-10\).
Calculate \(4\times23=92\), and \(92-10 = 82\).

Answer:

\(82\)