The point T is in the line SU, which means that it is between the points S and U. Therefore, the distance ST + TU must be equal to the distance between S and U. We know the distance between S and T and the distance between T and U, therefore:
[tex]ST\text{ + TU = SU}[/tex]Applying the data provided by the problem:
[tex]\begin{gathered} 3x\text{ + (4x + 1) = 8} \\ 3x\text{ + 4x + 1 = 8} \\ 7x\text{ = 8 -1} \\ 7x\text{ = 7} \\ x\text{ = }\frac{7}{7}\text{ = 1} \end{gathered}[/tex]We now need to find the distance between T and U, which is given by the following expression:
[tex]TU\text{ = 4x + 1}[/tex]Applying the data from x we calculated:
[tex]TU\text{ = 4}\cdot1\text{ + 1 = 4 + 1 = 5}[/tex]The numerical length of the line TU is 5.
