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

(1 point)
Responses

x= 9
x= 9

x=3
x=3

x = 1

1 answer

To find the value of \(x\) given that \(DO = 4x + 8\) and \(CO = 15x - 3\), we can set these two expressions equal to each other because \(O\) is the point where \(DO\) and \(CO\) meet, implying that they are two segments of the same side of the rectangle.

Thus, we can write the equation:

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

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

  1. Start by moving all terms involving \(x\) to one side of the equation and constants to the other side:

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

This simplifies to:

\[ 11 = 11x \]

  1. Now, divide both sides by 11:

\[ x = 1 \]

So, the value of \(x\) is \( \boxed{1} \).