Question

k = 13, kl = x + 18, and jl = 4x + 7, what is kl?
simplify your answer and write it as a proper fraction, mixed number, or in

Explanation:

Step1: Set up the equation

From the line - segment, \(JK + KL=JL\). Substitute \(JK = 13\), \(KL=x + 18\), and \(JL = 4x+7\) into the equation: \(13+(x + 18)=4x+7\).

Step2: Simplify the left - hand side

Combine like terms: \(13+x + 18=x+(13 + 18)=x + 31\). So the equation becomes \(x + 31=4x+7\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(x+31−x=4x + 7−x\), which gives \(31 = 3x+7\). Then subtract 7 from both sides: \(31−7=3x+7−7\), so \(24 = 3x\). Divide both sides by 3: \(x=\frac{24}{3}=8\).

Step4: Find \(KL\)

Substitute \(x = 8\) into \(KL=x + 18\). Then \(KL=8 + 18\).

Answer:

\(26\)