Solve for b based on the image below. Y is the midpoint of segment XZ, XY = 2b – 1, and YZ = 26 – 4b. You must show all work to receive credit. (If you prefer, you can write your work on paper, take a picture of it, and upload it below or send it to me in a webmail.)

Answer 1

To solve for \( b \), we will use the information given in the problem:

1. \( Y \) is the midpoint of segment \( XZ \), which means that the lengths \( XY \) and \( YZ \) are equal.
2. We are given two expressions for those lengths:
   • \( XY = 2b - 1 \)
   • \( YZ = 26 - 4b \)

Since \( Y \) is the midpoint of \( XZ \), we can set the two expressions equal to each other:

\[ XY = YZ \]

Substituting the expressions for \( XY \) and \( YZ \):

\[ 2b - 1 = 26 - 4b \]

Now, we will solve for \( b \):

1. First, add \( 4b \) to both sides:

\[ 2b + 4b - 1 = 26 \]

This simplifies to:

\[ 6b - 1 = 26 \]

2. Next, add \( 1 \) to both sides:

\[ 6b = 26 + 1 \]

\[ 6b = 27 \]

3. Now, divide by \( 6 \):

\[ b = \frac{27}{6} \]

4. Simplifying \( \frac{27}{6} \):

\[ b = \frac{9}{2} = 4.5 \]

Thus, the solution for \( b \) is:

\[ \boxed{4.5} \]