Suppose M is between L and N. Use the Segment Addition Postulate to solve for the variable. Then fine the lenghts of LM, MN, and LN.

LM=7y+9
MN=3y+4
LN=143

Please tell me how you got your answers.

To solve for the variable, we can use the Segment Addition Postulate, which states that if M is between L and N, then the sum of the lengths of LM and MN is equal to the length of LN.

In this case, we have:

LM + MN = LN

Substituting the given values, we have:

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

Combine like terms:

10y + 13 = 143

Now, we can solve for y:

10y = 143 - 13
10y = 130
y = 130/10
y = 13

Now, we can substitute the value of y back into the equations to find the lengths of LM, MN, and LN:

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

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

LN = 143 (already given)

Therefore, the lengths of LM, MN, and LN are:

LM = 100
MN = 43
LN = 143

To solve for the variable and find the lengths of LM, MN, and LN, we can use the Segment Addition Postulate. The Segment Addition Postulate states that for any three points on a line, the sum of the lengths of two smaller segments is equal to the length of the larger segment.

In this case, M is between L and N. According to the Segment Addition Postulate, the sum of the lengths of LM and MN should be equal to the length of LN.

So let's set up the equation using this information:

LM + MN = LN

Substituting the given values:

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

Now we will solve this equation to find the value of y.

Combining like terms, we get:

10y + 13 = 143

Next, subtract 13 from both sides:

10y = 143 - 13
10y = 130

Divide both sides of the equation by 10:

y = 13

Now that we have found the value of y, we can substitute it back into the expressions for the lengths of LM, MN, and LN.

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

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

LN = 143 (given in the question)

Hence, the lengths of LM, MN, and LN are:
LM = 100
MN = 43
LN = 143

LM+ MN=LN

LM + MN = 143
7y+9+3y+4=143
7y=9-9+3y+4-4= 143-9-4
7y+3y=130
10y=130
10y/10=130/10
y=13