Question

Given the rectangle ABCD as shown, find the value for x if DO=4x+8 and CO=15x−3 . (1 point) x=

Answer 1

To find the value of \( x \) given the lengths \( DO = 4x + 8 \) and \( CO = 15x - 3 \), we can equate the two expressions since both represent the length of the same segment \( O \) to points \( D \) and \( C \) in rectangle \( ABCD \).

Set the two expressions equal to one another:

\[
4x + 8 = 15x - 3
\]

Now, let's solve for \( x \).

1. First, subtract \( 4x \) from both sides:

\[
8 = 15x - 4x - 3
\]

This simplifies to:

\[
8 = 11x - 3
\]

2. Next, add 3 to both sides:

\[
8 + 3 = 11x
\]

This simplifies to:

\[
11 = 11x
\]

3. Finally, divide both sides by 11:

\[
x = 1
\]

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

\[
\boxed{1}
\]