Question

1. b is between a and c. ab = 2x + 1, bc = 3x − 4, and ac = 62. find the value of ‘x’, and determine if b is a bisector.

x = __________
bisector: yes or no?

Explanation:

Step1: Use segment addition postulate

Since \( B \) is between \( A \) and \( C \), we know that \( AB + BC = AC \). Substituting the given expressions, we get \((2x + 1)+(3x - 4)=62\).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 2x+3x + 1-4 = 62 \), which simplifies to \( 5x - 3 = 62 \). Add 3 to both sides: \( 5x=62 + 3=65 \). Then divide by 5: \( x=\frac{65}{5}=13 \).

Step3: Check if \( B \) is a bisector

Find \( AB \) and \( BC \) when \( x = 13 \). \( AB=2(13)+1 = 26 + 1=27 \). \( BC=3(13)-4 = 39 - 4=35 \). Since \( AB
eq BC \), \( B \) is not a bisector.

Answer:

\( x = 13 \)
Bisector: NO