Question

question 1 (3 points)
given: jk = 2x + 10, kl = x - 4, and jl = 21
use the picture and the given information to solve for x, jk an kl.
x =
jk =
kl =

Explanation:

Step1: Apply segment - addition postulate

Since $JL=JK + KL$, we substitute the given expressions: $21=(2x + 10)+(x - 4)$.

Step2: Simplify the right - hand side

Combine like terms: $21=2x+x + 10 - 4$, which simplifies to $21 = 3x+6$.

Step3: Solve for x

Subtract 6 from both sides: $21-6=3x$, so $15 = 3x$. Then divide both sides by 3: $x=\frac{15}{3}=5$.

Step4: Find JK

Substitute $x = 5$ into the expression for $JK$: $JK=2x + 10=2\times5+10=20$.

Step5: Find KL

Substitute $x = 5$ into the expression for $KL$: $KL=x - 4=5 - 4 = 1$.

Answer:

$x = 5$
$JK = 20$
$KL = 1$