Question

find jm. 6x + 7 4x + 5 j m l

Explanation:

Step1: Recognize M is midpoint

Since M is the midpoint of JL, \( JM = ML \). So \( 6x + 7 = 4x + 5 \)? Wait, no, wait—wait, actually, if M is the midpoint, then \( JM = ML \), so \( 6x + 7 = 4x + 5 \)? Wait, that would give negative x, which doesn't make sense. Wait, maybe I misread. Wait, the segments: JM is \( 6x + 7 \), ML is \( 4x + 5 \), and M is the midpoint, so \( JM = ML \). Wait, solving \( 6x + 7 = 4x + 5 \): subtract 4x: \( 2x + 7 = 5 \), subtract 7: \( 2x = -2 \), x = -1. But that would make lengths negative, which is impossible. Wait, maybe the labels are different? Wait, maybe JM and ML are equal, so maybe the equation is \( 6x + 7 = 4x + 5 \)? No, that can't be. Wait, maybe I made a mistake. Wait, perhaps the problem is that M is the midpoint, so \( JM = ML \), so \( 6x + 7 = 4x + 5 \)? Wait, no, maybe the other way. Wait, maybe the total length? No, the problem is to find JM. Wait, maybe the diagram has M as the midpoint, so JM = ML. So set \( 6x + 7 = 4x + 5 \). Wait, solving:

Step1: Set JM = ML (midpoint)

\( 6x + 7 = 4x + 5 \)

Step2: Solve for x

Subtract \( 4x \) from both sides: \( 2x + 7 = 5 \)

Subtract 7: \( 2x = -2 \)

Divide by 2: \( x = -1 \)

Wait, that gives JM = \( 6(-1) + 7 = 1 \), ML = \( 4(-1) + 5 = 1 \). Oh, okay, negative x but positive length. So then JM is 1? Wait, but let's check again.

Wait, maybe the problem is that M is the midpoint, so JM = ML. So \( 6x + 7 = 4x + 5 \). Solving:

\( 6x - 4x = 5 - 7 \)

\( 2x = -2 \)

\( x = -1 \)

Then JM = \( 6(-1) + 7 = -6 + 7 = 1 \)

Answer:

\( \boxed{1} \)