Math Problem Statement

If KL = 3x - 4, LM = x + 1, and KM = 5, what is KL?

Solution

To solve this, we need to use the information given in the problem.

  1. The total length of KMKM is 5.
  2. The segments are given as:
    • KL=3x4KL = 3x - 4
    • LM=x+1LM = x + 1

Since KL+LM=KMKL + LM = KM, we can set up the equation:

(3x4)+(x+1)=5(3x - 4) + (x + 1) = 5

Step-by-step solution:

  1. Combine like terms on the left-hand side: 4x3=54x - 3 = 5

  2. Add 3 to both sides: 4x=84x = 8

  3. Divide by 4 to solve for xx: x=2x = 2

Now, substitute x=2x = 2 into the expression for KLKL:

KL=3x4=3(2)4=64=2KL = 3x - 4 = 3(2) - 4 = 6 - 4 = 2

So, KL=2KL = 2.

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. If LMLM were doubled, how would that affect KLKL?
  2. What would KLKL be if KMKM were increased to 7?
  3. How does solving for xx affect the rest of the segment lengths?
  4. Can you explain how to verify your answer by adding KLKL and LMLM values?
  5. What would happen if one segment was unknown but KMKM was still given?

Tip: When solving for variables in geometry problems, always check if the total distance is consistent with the sum of the parts.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Linear Equations

Formulas

Sum of segment lengths: KL + LM = KM

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 7-9