Question

on a line segment, k is between j and l. if jk = x + 9, kl = 11, and jl = 2x + 19, what is jl? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment - addition postulate

Since $K$ is between $J$ and $L$, we have $JK + KL=JL$. Substitute the given expressions: $(x + 9)+11=2x + 19$.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side of the equation: $x+(9 + 11)=2x + 19$, which gives $x + 20=2x+19$.

Step3: Solve for $x$

Subtract $x$ from both sides of the equation: $x - x+20=2x - x + 19$, resulting in $20=x + 19$. Then subtract 19 from both sides: $20-19=x+19 - 19$, so $x = 1$.

Step4: Find the length of $JL$

Substitute $x = 1$ into the expression for $JL$. Since $JL=2x + 19$, then $JL=2\times1+19$. Calculate $2\times1+19=2 + 19=21$.

Answer:

21