Math Problem Statement

B is between A and C. If AB = x + 2, BC = 2x - 3, and AC = 5x - 7, what is AB?

Solution

The problem provided states:

  • AB=x+2AB = x + 2,
  • BC=2x3BC = 2x - 3,
  • AC=5x7AC = 5x - 7,
  • B is between A and C.

Since B is between A and C, we can use the property of segment addition, which states:

AB+BC=ACAB + BC = AC

Substituting the given expressions for ABAB, BCBC, and ACAC:

(x+2)+(2x3)=5x7(x + 2) + (2x - 3) = 5x - 7

Now, let's solve for xx.

x+2+2x3=5x7x + 2 + 2x - 3 = 5x - 7 3x1=5x73x - 1 = 5x - 7 1+7=5x3x-1 + 7 = 5x - 3x 6=2x6 = 2x x=3x = 3

Now that we know x=3x = 3, substitute it back into the expression for ABAB:

AB=x+2=3+2=5AB = x + 2 = 3 + 2 = 5

Thus, the length of ABAB is 5.

Would you like further details or explanations? Here are some related questions to deepen your understanding:

  1. What is the length of BCBC for this problem?
  2. Can you verify that AB+BC=ACAB + BC = AC using the values of xx and the corresponding segment lengths?
  3. How does the segment addition postulate apply in geometry?
  4. What happens to the length of ABAB if xx were a different value?
  5. Can we apply a similar process if BB were not between AA and CC?

Tip: When solving for unknowns in geometric problems, always check if all parts of the equation add up correctly using substitution.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Segment Addition Postulate

Formulas

AB + BC = AC

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 8-10