Question

find jk if k is between j and l. jk = 4x + 2, kl = 7x - 5, jl = 52 (you should draw and work this out on paper before answering.)

Explanation:

Step1: Use segment - addition postulate

Since $K$ is between $J$ and $L$, we have $JK + KL=JL$. Substitute the given expressions: $(4x + 2)+(7x - 5)=52$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $4x+7x+2 - 5=52$, which simplifies to $11x-3 = 52$.

Step3: Solve for $x$

Add 3 to both sides of the equation: $11x-3 + 3=52 + 3$, so $11x=55$. Then divide both sides by 11: $x=\frac{55}{11}=5$.

Step4: Find $JK$

Substitute $x = 5$ into the expression for $JK$. Since $JK = 4x+2$, then $JK=4\times5+2$. Calculate $4\times5+2=20 + 2=22$.

Answer:

22