Question

Given rectangle BCDA as shown, find the value of x if BE = 2x+9 and EC = 12x-11

(1 point)
x=

Answer 1

To find the value of \( x \) given the segments \( BE \) and \( EC \) in rectangle \( BCDA \), we know that:

1. The rectangle has two sides \( BC \) and \( CD \), and point \( E \) lies on line \( BC \).
2. The segments \( BE \) and \( EC \) must add up to the total length of \( BC \).

From the problem, we have:

\[ BE = 2x + 9 \]
\[ EC = 12x - 11 \]

Since point \( E \) is between points \( B \) and \( C \), we can write:

\[
BE + EC = BC
\]

However, we don't have the total length \( BC \). But since \( E \) lies on line \( BC \), for the sake of solving for \( x \), we'll equate the two segments, assuming they represent segments of the same length to some extent (implying it's just a common equation).

Thus, we can set up the equation:

\[
BE + EC = BC
\]

Assuming \( BE + EC = BC \) as a single value (and thus both expressions equating),

We can express the lengths as:

\[
2x + 9 + 12x - 11 = BC
\]

Since we don't have enough information to find BC directly, a possible equation would be to set the two expressions equal to each other to find when they equalize their respective points. Thus:

\[
2x + 9 = 12x - 11
\]

Now, we'll solve for \( x \):

1. Subtract \( 2x \) from both sides:

\[
9 = 10x - 11
\]

2. Add \( 11 \) to both sides:

\[
20 = 10x
\]

3. Divide by \( 10 \):

\[
x = 2
\]

Thus, the value of \( x \) is \( \boxed{2} \).