Question

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

Answer 1

To solve for \(b\), we start by using the information given in the problem.

1. **Understanding the Problem**:
We know that \(Y\) is the midpoint of segment \(XZ\). Thus, the lengths of the segments \(XY\) and \(YZ\) will be equal:
\[
XY = YZ
\]

2. **Setting Up the Equation**:
We are given:
\[
XY = 2b - 1
\]
\[
YZ = 26 - 4b
\]
Since \(Y\) is the midpoint, we set the two expressions equal to each other:
\[
2b - 1 = 26 - 4b
\]

3. **Solving the Equation**:
Now, we will solve the equation step by step:

**Step 1**: Add \(4b\) to both sides:
\[
2b + 4b - 1 = 26
\]
This simplifies to:
\[
6b - 1 = 26
\]

**Step 2**: Add \(1\) to both sides:
\[
6b = 26 + 1
\]
This simplifies to:
\[
6b = 27
\]

**Step 3**: Divide both sides by \(6\):
\[
b = \frac{27}{6}
\]
Simplifying the fraction gives:
\[
b = \frac{9}{2} \quad \text{or} \quad b = 4.5
\]

4. **Final Answer**:
Therefore, the solution for \(b\) is:
\[
b = 4.5
\]