Question

M is the midpoint of LN. If LM = 5x - 10 and 2x + 2. what is LN? LN =

Answer 1

Since M is the midpoint of LN, LM = MN. By solving 5x - 10 = 2x + 2, we find x = 4. Therefore, LM and MN are each 10, making the entire length of LN equal to 20.

Step-by-step explanation:

To find the length of the entire segment LN, we first need to know that since M is the midpoint of LN, LM and MN are equal in length. Given that LM is 5x - 10 and MN is given as 2x + 2, setting these two expressions equal will allow us to solve for x.

Equating the two expressions we have:
5x - 10 = 2x + 2

Solving for x will give us:
3x = 12
x = 4

Now, we can find the length of LM and MN using the value of x:
LM = 5x - 10 = 5(4) - 10 = 20 - 10 = 10
MN = 2x + 2 = 2(4) + 2 = 8 + 2 = 10

The length of LN, which is the sum of LM and MN, is therefore:
LN = LM + MN = 10 + 10 = 20.

Answer 2

Given:

Midpoint of LN = M

LM = 5x - 10

MN = 2x + 2

Since M is the midpoint of LN, it means that M divides LN by 2 equal sides.

It is represented graphically as:

Since LM and MN are equal, We have:

LM = MN

5x - 10 = 2x + 2

Let's solve for x.

Add 10 t0 both sides:

5x - 10 + 10 = 2x + 2 + 10

5x = 2x + 12

Subtract 2x from both sides:

5x - 2x = 2x - 2x + 12

3x = 12

Divide both sides by 3:

`\begin{gathered} (3x)/(3)=(12)/(3) \\ \\ x=4 \end{gathered}`

Input 4 for x to find LM and MN.

LM = 5x - 10

= 5(4) - 10

= 20 - 10

= 10

MN = 2x + 2

= 2(4) + 2

= 8 + 2

= 10

LN = LM + MN

= 10 + 10

= 20

ANSWER:

LN = 20