Final answer:
The value of x for the three sets of equations were found by summing RS and ST to equal RT and solving for x. For the first set, x equals 12. The third set yields x as 2, while the second set has a discrepancy in the options provided.
Step-by-step explanation:
To solve for x in each set of equations, we use the fact that RT is the sum of RS and ST. For instance, in the first set, RT = RS + ST, which translates to 60 = 3x - 16 + 4x - 8. Combining like terms and solving for x gives us the solution.
First Set
RT = RS + ST
60 = 3x - 16 + 4x - 8
60 = 7x - 24
7x = 60 + 24
7x = 84
x = 84 / 7
x = 12
Second Set
RT = RS + ST
3x - 4 = 2x - 8 + 11
3x - 4 = 2x + 3
x = 3 + 4
x = 7 (Not among the options, potentially an error in the provided options or in the original equations.)
Third Set
RT = RS + ST
5x + 14 = 4x + 4 + 7x - 2
5x + 14 = 11x + 2
6x = 12
x = 12 / 6
x = 2
By following these steps to rearrange the equations and solve for x, we can determine the correct value of x for each set of line segments.