Question 13

Question

A)

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 \( x \), we need to set the two expressions for the lengths \( BE \) and \( EC \) equal to each other. In a rectangle, if \( E \) is a point on side \( BC \), then the entire side \( BC \) can be expressed as the sum of \( BE \) and \( EC \):

\[ BC = BE + EC \]

Assuming \( BC \) is a straight line and point \( E \) divides it into segments \( BE \) and \( EC \), we can set up the equation:

\[ BE + EC = BC \]

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

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

Since we need the lengths of \( BE \) and \( EC \) individually for equality, we recognize that \( BE + EC \) represents the total length \( BC \). Thus:

\[ BE = EC \]

Setting up the equation yields:

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

Now we solve for \( x \):

1. Rearranging the equation:

\[ 2x + 9 - 12x + 11 = 0 \] \[ -10x + 20 = 0 \]

2. Isolating \( x \):

\[ -10x = -20 \] \[ x = 2 \]

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

\[ \boxed{2} \]