The value of the line segment MN is 7.
In the question, we are given a line segment MN, with a point T in between them, dividing the line segment into MT and NT.
Also, we are given that NT = x + 5, MN = 3x, and MT = 7.
As the line segment, MN is divided into two segments MT and NT, we can write that:
MN = MT + NT.
Putting the values MN = 3x, NT = x + 5, and MT = 7, we get:
3x = 7 + (x + 5),
or, 3x = 12 + x,
or, 3x - x = 12,
or, 2x = 26,
or, x = 26/2,
or, x = 13.
Now, we know that MN = 3x.
Putting the value of x = 7 in MN, we get:
MN = 3*7,
or, MN = 21.
Thus, the value of the line segment MN is 7.
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