Question

Solve for b based on the image below. Y is the midpoint of segment XZ, XY = 2b – 1, and YZ = 26 – 4b

Answer 1

To solve for \( b \), we know that \( Y \) is the midpoint of segment \( XZ \). By the definition of a midpoint, the lengths of the segments \( XY \) and \( YZ \) should be equal. Therefore, we can set up the following equation:

\[
XY = YZ
\]

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

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

Now, we can solve for \( b \). First, we add \( 4b \) to both sides:

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

This simplifies to:

\[
6b - 1 = 26
\]

Next, we add \( 1 \) to both sides:

\[
6b = 27
\]

Now, we divide both sides by \( 6 \):

\[
b = \frac{27}{6} = \frac{9}{2} = 4.5
\]

Thus, the value of \( b \) is:

\[
\boxed{4.5}
\]