To find the value of \( x \) given the equations for \( A \) and \( B \), we need to set the two expressions equal to each other because they represent the same segment.
The equations provided are:
\[ A = 9x + 28 \] \[ B = 1x \]
Assuming \( A \) and \( B \) are equal, we can set them up as follows:
\[ 9x + 28 = 1x \]
Now, let's solve for \( x \).
- First, subtract \( 1x \) from both sides to isolate terms involving \( x \):
\[ 9x - 1x + 28 = 0 \]
This simplifies to:
\[ 8x + 28 = 0 \]
- Next, subtract 28 from both sides:
\[ 8x = -28 \]
- Finally, divide both sides by 8:
\[ x = \frac{-28}{8} = -\frac{7}{2} = -3.5 \]
Thus, the value of \( x \) is:
\[ \boxed{-3.5} \]
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