Final answer:
To find the value of x for congruent segments RS and ST, the expressions for their measures (3x - 48 and 9x) are set equal. Solving the resulting equation, x is found to be -8.
Step-by-step explanation:
A student is asking for help in solving for the value of x in two congruent segments, RS and ST, with provided expressions for their measures, MRST = 3x - 48 and STU = 9x. Since RS is congruent to ST, their measures are equal, so we can set the two expressions equal to each other to solve for x:
3x - 48 = 9x
Subtract 3x from both sides to get:
-48 = 6x
Now, divide both sides by 6:
x = -8
Thus, the value of x that makes the segments congruent is -8.