Final answer:
To find the value of x, set up an equation using the given information and then solve for x by combining like terms and isolating the variable.
Step-by-step explanation:
To find the value of x, we need to set up an equation using the information given in the question. We know that line OP bisects line LM at M, so ML and LN are equal. From the given information, we have ML = 3(3x-1) and LN = 5(2+2x).
Setting these two expressions equal to each other, we get 3(3x-1) = 5(2+2x).
Simplifying this equation, we have 9x - 3 = 10 + 10x.
Moving all the x terms to one side and all the constant terms to the other side, we have 9x - 10x = 10 + 3.
Combining like terms, we get -x = 13.
Dividing both sides of the equation by -1, we find that x = -13.