Suppose M is between L and N, Use segment addition postulate to solve the variable.Find lenght of LM, MN, LN

Question

1) LM = 3x+8
MN= 2x-5
LN= 23

2) LM= 7y+9
MN- 3y+4
LN=143

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

Answer 1

LM = 3x + 8
MN = 2x - 5
LN = 23

Using the segment addition postulate:

LM + MN = LN

Therefore:

3x + 8 + (2x - 5) = 23

Combine like terms:

5x + 8 - 5 = 23

Subtract 5 from 8:

5x + 3 = 23

Subtract 3 from both sides:

5x = 20

Divide by 5 on both sides to solve for x:

x = 4

Now to find LM and MN, plug x into the expressions:

LM = 3x + 8
= 3(4) + 8
= 12 + 8
= 20

MN = 2x - 5
= 2(4) - 5
= 8 - 5
= 3

So, this is your answer:

LM = 20
MN = 3
LN = 23

For the next question, use the same process:

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

Combine like terms:

10y + 9 + 4 = 143

Add 9 and 4:

10y + 13 = 143

Subtract 13 from both sides:

10y = 130

Divide by 10 on both sides to solve for y:

y = 13

Now, plug this into the previous expressions:

LM = 7y + 9
= 7(13) + 9
= 91 + 9
= 100

MN = 3y + 4
= 3(13) + 4
= 39 + 4
= 43

So:

LM = 100
MN = 43
LN = 143

For the final problem, the equation is a little different, but the basic methods are still used:

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

Combine like terms:

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

Add 3/2 and 2:

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

Subtract 3 1/2z from both sides and combine like terms:

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

Subtract 2 from both sides:

1 1/2 = 1 1/2z

Divide by 1 1/2 to solve for z:

1 = z

Now, you have to plug this into all 3 expressions (not just 2 this time):

LM = 1/2z + 2
= 1/2(1) + 2
= 1/2 + 2
= 2 1/2

MN = 3z + 3/2
= 3(1) + 3/2
= 3 + 3/2
= 4 1/2

LN = 5z + 2
= 5(1) + 2
= 5 + 2
= 7

So, this is your answer:

LM = 2 1/2
MN = 4 1/2
LN = 7

Hope this helps!

Answer 2

just solve for X. since you know LN is the whole line you will make the equation LN = MN+LM 23=2x-5+3x+8 23=5x+3 20=5x x=4 so then plug back in. LM=3(4)+8 = 20 MN = 2(4)-5=3 LN=23

Answer 3

1) LM = 3x+8
MN= 2x-5
LN= 23
3x+8 +2x-5=23
5x= 20 -->x =4
LM = 20 and MN = 3

2) LM= 7y+9
MN- 3y+4
LN=143
7y+9+3y+4 =143
10y = 130 --> y = 13
LM = 7*13+9 =100 and MN = 43


3) LM= 1/2z +2
MN= 3z + 3/2
LN = 5z +2
.5z +2 +3z +3.5 = 5z+2
-1.5z = -1.5
z = 1
LM = 2.5 and MN = 4.5 and LN = 7