Question

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

Answer 1

To solve for \( x \), we can use the information given about segments \( BE \) and \( EC \).

Since \( E \) is a point on the line segment \( BC \) in rectangle \( BCDA \), we know that \( BE + EC = BC \).

1. Set up the equation based on the segments:
\[
BE + EC = BC
\]
Substituting the expressions for \( BE \) and \( EC \):
\[
(2x + 9) + (12x - 11) = BC
\]

2. Combine like terms:
\[
2x + 12x + 9 - 11 = BC
\]
\[
14x - 2 = BC
\]

Now, since \( BC \) is a fixed length in the rectangle, we don't know its numerical value from the problem, but we can set \( BC \) on one side of the equation to separate \( x \):

3. There is no separate value for \( BC \) provided in the problem. We need to equate the sum of \( BE \) and \( EC \) to keep the expressions consistent:
\[
2x + 9 + 12x - 11 = 0
\]

This method only makes sense if we set \( BC = 0 \) or treat it as a functional relationship. So simplifying:
\[
14x - 2 = 0
\]

Thus:
\[
14x = 2
\]
\[
x = \frac{2}{14} = \frac{1}{7}
\]

4. Therefore, the final solution for \( x \) is:
\[
x = \frac{1}{7}
\]

If you have any additional constraints or values for \( BC \), please provide those for a more accurate solution.