*Addition Postulate problem this time they are all problems.?

Question

Suppose M is between L and N. Use the segment Addition Postulate to solve for the variable. Then find the lengths of line: LM MN and LN

LM = 1/2z + 2
MN = 3z + 3/2
LN = 5z + 2

Answer 1

If M is between L and n, then the segment addition postulate says that LM + MN = LN.
So (1/2z + 2) + (3z + 3/2) = 5z + 2, or 5z - 1/2z - 3z = 2 + 3/2 - 2.
Then 3/2z = 3/2 and so z = 1.
Thus LM = 1/2 + 2 = 2 1/2
MN = 3 + 3/2 = 4 1/2
and LN = 5 + 2 = 7,
and in fact 2 1/2 + 4 1/2 = 7 really is true.

Answer 2

LM + MN = LN
=>1/2z + 2 + 3z + 3/2 = 5z + 2

=>2 + 3/2 - 2 = 5z - 1/2z - 3z
=>3/2 = 2z - 1/2z
=>3/2 = z(2-1/2)
=>3/2 = z(3/2)
=>1 = z
LM = 5/2
MN=9/2
LN=7

Answer 3

Using the addition postulate (which states one part of a line + another part of the line = the whole line), you get LM+MN=LN. This comes out to be:

1/2z+2+3z+3/2=5z+2

Combine like terms

-3/2z=-3/2

Divide both sides by -3/2

z=1

Therefore, LM=2.5, MN=4.5, and LN=7

LOL, I answered this in your other post too. :-)