# Chapter 2 - Reasoning and Proof - 2-5 Reasoning in Algebra and Geometry - Practice and Problem-Solving Exercises: 23

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \text{KM = 35} & \text{Given} \\2 & \text{KL + LM = KM} & \text{Segment Addition Postulate} \\3 & \text{2x - 5 + 2x = 35} & \text{Substitution Property} \\4 & \text{4x - 5 = 35} & \text{Distributive Property} \\5 & \text{4x = 40} & \text{Addition Property of Equality} \\6 & \text{x = 10} & \text{Division Property of Equality} \\7 & \text{KL = 2x - 5} & \text{Given} \\8 & \text{KL = 2(10) - 5} & \text{Substitution Property} \\9 & \text{KL = 15} & \text{Simplify} \end{array}

#### Work Step by Step

Substitute the lengths shown in the diagram and solve for x. Use the value that you found for x to find the length of $\overline{KL}$.

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