Need help with geometry?

Question

suppose M is between L and N. use the Segment Addition Postulate to solve for the variable. then find the lengths of LM, MN, LN.

1. LM= 7y+9

MN= 3y+4

LN= 143

2. LM= 1/2z+2

MN= 3z+3/2

LN= 5z+2

Answer 1

1 i think is 13  

Answer 2

LM + MN = LN

(7y + 9) + (3y + 4) = 143

Simplify: 7y + 3y + 9 + 4 = 143

10y + 13 = 143

Subtract 13 from both sides

10y = 130

y = 13

LM = 1/2z + 2

MN = 3z + 3/2

LN = 5z + 2

LM + MN = LN

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

Multiply by 2 to reduce/eliminate the denominators

2 x [(1/2z + 2) + (3z + 3/2)] = 2 x (5z + 2)

(z + 4) +  (6z + 3) = 10z + 4

7z + 7 = 10z + 4

Subtract 7z

7 = 3z + 4

Subtract 4

3 = 3z

1 = z

CHECK: (1/2z + 2) + (3z + 3/2) = 5z + 2

1/2 (1) + 2 + 3(1) + 3/2 = 5(1) + 2

  1/2 + 2 + 3 + 3/2 = 7

5 + 4/2 = 7

5 + 2 = 7

7 = 7

The answer checks out.

Answer 3

I believe what you are saying is that "m" lies on a line between l and n.  If that is so, then lm + mn = ln or 7y + 9 + 3y + 4 = 143.

Solving for y:

10y + 13 = 143

y = 13

Then plug n for y to get lengths for lm and mn.  

For part 2, by the same reasoning, 1/2z + 2 + 3z + 3/2 = 5z + 2

Solving for z:

1.5z = 3/2

z = 1

Then, plug in z to get the lengths of lm, mn, and ln.