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13 of 1913 of 19 Items which is the true correct answer and why

Question

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

(1 point)
x=

1 answer

To solve for \( x \) in the problem, we know the following:

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

Since \( E \) is a point on line \( BC \) that divides it into two segments, we can use the fact that the whole length of \( BC \) is the sum of \( BE \) and \( EC \). Therefore, we can write the equation:

\[ BE + EC = BC \]

However, since we don't have the total length of \( BC \), we will assume that \( E \) is the endpoint of those segments. According to the problem assumption, we can write the equation:

\[ BE = EC \]

Now substitute the expressions for \( BE \) and \( EC \):

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

Now, we will solve for \( x \):

  1. Rearranging the equation to isolate \( x \):

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

  1. Simplifying:

\[ 20 = 10x \]

  1. Divide by 10:

\[ x = 2 \]

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