The value of x is -18.
In the given diagram, we are told that JK is congruent to GI. We need to solve for the value of x using the given information.
Let's break down the given information:
- HJ = 3x
- HK = 2x
- KI = 6x
- JG = 18 units
Since JK is congruent to GI, we can equate the lengths of these line segments:
HJ + JK = JG + GI
Substituting the given values, we get:
3x + 2x = 18 + 6x
Combining like terms, we have:
5x = 18 + 6x
To solve for x, we can subtract 6x from both sides of the equation:
5x - 6x = 18
Simplifying further, we get:
-x = 18
To solve for x, we multiply both sides of the equation by -1 to isolate x:
x = -18