Question

let jl = 24. find x and the missing segment lengths. #8: x = ___ your answer #8: jk = _ your answer #8: kl = ___ * your answer

Explanation:

Step1: Set up equation

Since $JL = JK+KL$ and $JL = 24$, $JK=4x - 3$, $KL=x + 2$, we have the equation $(4x - 3)+(x + 2)=24$.
Simplify the left - hand side: $4x-3+x + 2=5x-1$. So, $5x-1 = 24$.

Step2: Solve for x

Add 1 to both sides of the equation $5x-1 = 24$: $5x-1+1=24 + 1$, which gives $5x=25$.
Divide both sides by 5: $\frac{5x}{5}=\frac{25}{5}$, so $x = 5$.

Step3: Find JK

Substitute $x = 5$ into the expression for $JK$. $JK=4x-3=4\times5-3=20 - 3=17$.

Step4: Find KL

Substitute $x = 5$ into the expression for $KL$. $KL=x + 2=5+2=7$.

Answer:

$x = 5$
$JK = 17$
$KL = 7$