Question

question point k is on line segment $overline{jl}$. given $kl = 2x - 2$, $jl = 4x + 9$, and $jk = 5x + 2$, determine the numerical length of $overline{jl}$. answer attempt 1 out of 2 $jl=$

Explanation:

Step1: Use segment - addition postulate

Since point $K$ is on line segment $\overline{JL}$, we have $JK + KL=JL$. Substitute the given expressions: $(5x + 2)+(2x - 2)=4x + 9$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+2 + 2x-2=7x$. So the equation becomes $7x=4x + 9$.

Step3: Solve for $x$

Subtract $4x$ from both sides: $7x-4x=4x + 9-4x$, which gives $3x=9$. Then divide both sides by 3: $x = 3$.

Step4: Find the length of $JL$

Substitute $x = 3$ into the expression for $JL$. Since $JL=4x + 9$, then $JL=4\times3+9=12 + 9=21$.

Answer:

$21$