In quadrilateral FGKJ , FK¯¯¯¯¯¯¯¯ is a perpendicular bisector of GJ¯¯¯¯¯¯¯ . The length of segment GF¯¯¯¯¯¯¯¯ is 6+x units, and the length of segment JF¯¯¯¯¯¯¯ is 3x−5 units. What is the value of x? (1 point)

Answer 1

To solve for \( x \) in the quadrilateral \( FGKJ \), where \( FK \) is the perpendicular bisector of \( GJ \), we can apply the property of the perpendicular bisector: any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects.

Given that \( GF = 6 + x \) and \( JF = 3x - 5 \), we know:

\[ GF = JF \]

Therefore, we can set the two expressions equal to each other:

\[ 6 + x = 3x - 5 \]

Next, we can rearrange this equation to isolate \( x \). Start by subtracting \( x \) from both sides:

\[ 6 = 3x - x - 5 \]

This simplifies to:

\[ 6 = 2x - 5 \]

Now, add 5 to both sides:

\[ 6 + 5 = 2x \]

Resulting in:

\[ 11 = 2x \]

Now, divide both sides by 2:

\[ x = \frac{11}{2} \] \[ x = 5.5 \]

Thus, the value of \( x \) is \( \boxed{5.5} \).