Question

point j is on line segment ik. given jk = 2x - 1, ik = 3x + 2, and ij = 3x - 5, determine the numerical length of jk.

Explanation:

Step1: Use segment addition postulate

Since \( J \) is on \( \overline{IK} \), we have \( IJ + JK = IK \). Substitute the given expressions: \( (3x - 5) + (2x - 1) = 3x + 2 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 3x - 5 + 2x - 1 = 3x + 2 \) → \( 5x - 6 = 3x + 2 \). Subtract \( 3x \) from both sides: \( 2x - 6 = 2 \). Add 6 to both sides: \( 2x = 8 \). Divide by 2: \( x = 4 \).

Step3: Find \( JK \) length

Substitute \( x = 4 \) into \( JK = 2x - 1 \): \( JK = 2(4) - 1 = 8 - 1 = 7 \).

Answer:

7