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Question


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

(1 point)
x=

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Answer 1

To find the value of \( x \) in the problem, we know that point \( E \) divides the segment \( BC \) into two parts: \( BE \) and \( EC \). Since \( E \) lies between \( B \) and \( C \), we can set up the equation:

\[
BE + EC = BC
\]

Given:
- \( BE = 2x + 9 \)
- \( EC = 12x - 11 \)

Assuming \( BC \) represents the total length of the segment from \( B \) to \( C \), the equation becomes:

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

Simplifying the equation yields:

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

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

\[
14x - 2 = BC
\]

Since nothing is specified for \( BC \), we can focus on setting the two segments equal, since they must add up correctly. If \( BC \) can be defined as only relying on \( BE \) and \( EC \) we would usually tough it to an assumed equality similar to \( 0 \) or \( 1 \).

For finding \( x \), we equate \( BE \) and \( EC \):

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

Now solve for \( x \):

1. Move all \( x \) terms to one side and constant terms to the other:

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

\[
20 = 10x
\]

2. Divide both sides by \( 10 \):

\[
x = 2
\]

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

\[
\boxed{2}
\]