Question

if (jk = 10x), (kl=5x + 14), and (jl = 20x-6), what is (jk)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $JL=JK + KL$, we substitute the given expressions: $20x-6=10x+(5x + 14)$.

Step2: Simplify the right - hand side

$20x-6=10x + 5x+14$, which simplifies to $20x-6=15x + 14$.

Step3: Isolate the variable $x$

Subtract $15x$ from both sides: $20x-15x-6=15x-15x + 14$, resulting in $5x-6=14$.
Then add 6 to both sides: $5x-6 + 6=14 + 6$, so $5x=20$.

Step4: Solve for $x$

Divide both sides by 5: $\frac{5x}{5}=\frac{20}{5}$, and $x = 4$.

Step5: Find the length of $JK$

Substitute $x = 4$ into the expression for $JK$. Since $JK = 10x$, then $JK=10\times4=40$.

Answer:

40