how do you do segements in 10th grade math?

Question

if T is the midpoint of SU, find the values of x and ST.
S T U
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3x + 5 4x - 1

Answer 1

OK, to do this, you need to realize the following:
If T is the midpoint, then ST must equal TU. (ST = TU)

From here, it's straight algebra:
ST = 3x+5
TU = 4x-1
ST = TU = 3x + 5 = 4x - 1
3x + 5 = 4x - 1
3x - 3x + 5 + 1 = 4x - 3x - 1 + 1
6 = x (solution!)

If 6 = x, and ST = 3x + 5:
ST = 3x + 5 = 3 * 6 + 5 = 23 (solution!)