The given information about the midpoint of the line segment RS, and the values of RM = x + 6 and RS = 5x + 3 gives us the missing values as: RM = 9, MS = 9, and RS = 18.
In the question, we are given that M is the midpoint of the line segment RS.
We are asked to find the missing value of MS, using the given information RM = x + 6 and RS = 5x + 3.
Since M is the midpoint of RS, we can say that the segment on the left of M will be equal to the segment to the right of M.
Thus, we get RM = MS.
But, we are given that RM = x + 6.
Thus, we have RM = MS = x + 6.
Also, RM and MS together forms RS.
Thus, we can write that:
RS = RM + MS.
Substituting the known values, we get:
5x + 3 = x + 6 + x + 6,
or, 5x + 3 = 2x + 12,
or, 5x - 2x = 12 - 3,
or, 3x = 9,
or, x = 9/3,
or, x = 3.
Using the value of x = 3, we can get:
RM = x + 6 = 3 + 6 = 9.
MS = x + 6 = 3 + 6 = 9.
RS = 5x + 3 = 5*3 + 3 = 15 + 3 = 18.
Thus, the given information about the midpoint of the line segment RS, and the values of RM = x + 6 and RS = 5x + 3 gives us the missing values as: RM = 9, MS = 9, and RS = 18.
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