Final answer:
To find the value of x, the two expressions for segments rs and rt of the same line are set equal to each other. After simplifying the equation 3(x - 4) = 3(2x - 9), x is solved for and is found to be equal to 5.
Step-by-step explanation:
The question involves finding the value of x given two algebraic expressions for rs and rt. To solve this, we must first equate the two expressions since they both represent segments of a line, assuming they are equal to each other. This will give us a single equation in terms of x that can be manipulated to isolate and solve for x.
First, we write down the given expressions: rs = 3(x - 4) and rt = 3(2x - 9). By setting them equal to each other, because the segments rs and rt are parts of the same line, we get the equation 3(x - 4) = 3(2x - 9). Simplifying and solving, we can find the value for x.
Expanding both sides of the equation gives us 3x - 12 = 6x - 27. Bringing all terms involving x to one side and constants to the other side, we have 3x - 6x = -27 + 12. Simplifying that, we get -3x = -15, and by dividing each side by -3, we find x = 5.