Question

if (jl = 5x + 2), find (jl).
27
(3x - 1)
j
k
l

Explanation:

Step1: Set up equation based on segment - addition postulate

Since $JL=JK + KL$, we have $5x + 2=27+(3x - 1)$.

Step2: Simplify the right - hand side of the equation

$5x + 2=27 + 3x-1$, which simplifies to $5x + 2=3x + 26$.

Step3: Isolate the variable $x$

Subtract $3x$ from both sides: $5x-3x + 2=3x-3x + 26$, resulting in $2x+2 = 26$. Then subtract 2 from both sides: $2x+2 - 2=26 - 2$, so $2x=24$.

Step4: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{24}{2}$, giving $x = 12$.

Step5: Find the length of $JL$

Substitute $x = 12$ into the expression for $JL$: $JL=5x + 2=5\times12+2=60 + 2=62$.

Answer:

62