Question

if $jk = 6x$, $kl = 10x - 7$, and $jl = 9$, what is $jk$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the segment addition postulate, \( JK + KL = JL \). Substituting the given expressions, we get \( 6x+(10x - 7)=9 \).

Step2: Simplify the equation

Combine like terms: \( 16x-7 = 9 \).

Step3: Solve for x

Add 7 to both sides: \( 16x=9 + 7=16 \). Then divide both sides by 16: \( x = \frac{16}{16}=1 \).

Step4: Find JK

Since \( JK = 6x \) and \( x = 1 \), substitute \( x \) into the expression for \( JK \): \( JK=6\times1 = 6 \).

Answer:

\( 6 \)