Question

point k is on line segment $overline{jl}$. given $jk = 2x, kl = x + 3$, and $jl = 4x$, determine the numerical length of $overline{kl}$.

Explanation:

Step1: Use segment - addition postulate

Since point K is on line segment $\overline{JL}$, we have $JK + KL=JL$. Substituting the given expressions: $2x+(x + 3)=4x$.

Step2: Simplify the left - hand side of the equation

Combining like terms, $2x+x+3 = 3x + 3$. So, $3x+3 = 4x$.

Step3: Solve for x

Subtract $3x$ from both sides of the equation: $3x+3-3x=4x - 3x$, which gives $x = 3$.

Step4: Find the length of $\overline{KL}$

Substitute $x = 3$ into the expression for $KL$. Since $KL=x + 3$, then $KL=3+3=6$.

Answer:

6