Math Problem Statement

If KL = 10x − 19, LM = 1, and KM = 5x − 8, what is KM?

10x − 19 K 1 L M 5x −

Solution

Given the information, we can use the relationship between the segments KL, LM, and KM to solve for xx and find the length of KM.

Step 1: Set up the equation

The total length of segment KMKM is equal to the sum of the lengths of segments KLKL and LMLM: KM=KL+LMKM = KL + LM We are given the following:

  • KL=10x19KL = 10x - 19
  • LM=1LM = 1
  • KM=5x8KM = 5x - 8

Using the equation KM=KL+LMKM = KL + LM: 5x8=(10x19)+15x - 8 = (10x - 19) + 1

Step 2: Simplify the equation

Simplify the right-hand side: 5x8=10x19+15x - 8 = 10x - 19 + 1 5x8=10x185x - 8 = 10x - 18

Step 3: Solve for xx

Now, subtract 5x5x from both sides to get: 8=5x18-8 = 5x - 18

Add 18 to both sides: 10=5x10 = 5x

Divide by 5: x=2x = 2

Step 4: Find KMKM

Now that we know x=2x = 2, substitute it back into the expression for KMKM: KM=5x8=5(2)8=108=2KM = 5x - 8 = 5(2) - 8 = 10 - 8 = 2

So, KM=2KM = 2.

Would you like more details or have any questions?

Related Questions:

  1. What would the value of KLKL be if x=2x = 2?
  2. How do you solve similar problems involving segment addition postulates?
  3. Can the values of LMLM and KMKM change, and how would that affect xx?
  4. What are some real-world applications of segment addition postulates?
  5. How do you verify your results in problems involving algebraic expressions?

Tip:

Always double-check your algebraic manipulations, especially when combining like terms or moving variables across the equation!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Segment Addition Postulate

Formulas

KM = KL + LM
KL = 10x - 19
LM = 1
KM = 5x - 8

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 8-10