Question

The picture is not drawn to scale. Find the value of 𝑥xx if 𝐴=9𝑥+28A=9x+28A=9x+28 and 𝐵=1𝑥B=1xB=1x .

Answer 1

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 \( x \).

1. First, subtract \( 1x \) from both sides to isolate terms involving \( x \):

\[
9x - 1x + 28 = 0
\]

This simplifies to:

\[
8x + 28 = 0
\]

2. Next, subtract 28 from both sides:

\[
8x = -28
\]

3. Finally, divide both sides by 8:

\[
x = \frac{-28}{8} = -\frac{7}{2} = -3.5
\]

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

\[
\boxed{-3.5}
\]