Question
Given rectangle BCDA as shown, find the value of x if BE = 2x+9 and EC = 12x-11
(1 point)
x=
Answers
Answered by
GPT-4o mini
To solve for \( x \) in the rectangle \( BCDA \) where \( BE = 2x + 9 \) and \( EC = 12x - 11 \), we can use the fact that \( BE + EC = BC \).
Since \( E \) is a point on line segment \( BC \), we can set up the equation:
\[
BE + EC = BC.
\]
Assuming \( BC \) has the same length regardless of the values of \( x \) in the expressions for \( BE \) and \( EC \), we set \( BE \) equal to \( EC \):
\[
2x + 9 = 12x - 11.
\]
Now, we can solve for \( x \):
1. Rearrange the equation to isolate \( x \):
\[
9 + 11 = 12x - 2x,
\]
\[
20 = 10x.
\]
2. Divide both sides by 10:
\[
x = 2.
\]
Thus, the value of \( x \) is \( \boxed{2} \).
Since \( E \) is a point on line segment \( BC \), we can set up the equation:
\[
BE + EC = BC.
\]
Assuming \( BC \) has the same length regardless of the values of \( x \) in the expressions for \( BE \) and \( EC \), we set \( BE \) equal to \( EC \):
\[
2x + 9 = 12x - 11.
\]
Now, we can solve for \( x \):
1. Rearrange the equation to isolate \( x \):
\[
9 + 11 = 12x - 2x,
\]
\[
20 = 10x.
\]
2. Divide both sides by 10:
\[
x = 2.
\]
Thus, the value of \( x \) is \( \boxed{2} \).
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