Point M lies between points L and N on Line segment L N .
The space between L and M is 10 x + 8. The space between M and N is 5 x minus 4.
If LN = 12x + 16, what is the length of Line segment L N in units?
16 units
40 units
48 units
64 units
We are given that the space between L and M is 10x + 8, and the space between M and N is 5x - 4. Since M lies between L and N, we can express the length of LN as the sum of the two spaces: LN = (10x + 8) + (5x - 4).
Simplifying the expression, we get:
LN = 10x + 8 + 5x - 4
LN = 15x + 4
We are also given that LN = 12x + 16.
Setting the two expressions equal to each other, we have:
12x + 16 = 15x + 4
Subtracting 12x from both sides, we get:
16 = 3x + 4
Subtracting 4 from both sides, we get:
12 = 3x
Dividing both sides by 3, we get:
4 = x
Now, we can substitute the value of x back into the expression for LN:
LN = 15x + 4
LN = 15(4) + 4
LN = 60 + 4
LN = 64
Therefore, the length of line segment LN is 64 units. Answer: \boxed{64 \text{ units}}.
To find the length of line segment LN, we need to add the lengths of LM and MN.
Given:
The space between L and M is 10x + 8.
The space between M and N is 5x - 4.
The length of LN is 12x + 16.
Let's set up the equation to find the length of LM:
LM = 10x + 8
And the equation to find the length of MN:
MN = 5x - 4
The total length of LN is the sum of LM and MN, so we can set up the equation:
LN = LM + MN
Substituting the given expressions for LM and MN, we have:
12x + 16 = (10x + 8) + (5x - 4)
Now, let's solve for x:
12x + 16 = 10x + 8 + 5x - 4
12x + 16 = 15x + 4
Subtracting 12x from both sides:
16 = 15x + 4 - 12x
16 = 3x + 4
Subtracting 4 from both sides:
12 = 3x
Dividing both sides by 3:
x = 4
Now that we have the value of x, we can substitute it back into the equation for LN to find the length of line segment LN:
LN = 12x + 16
LN = 12(4) + 16
LN = 48 + 16
LN = 64 units
Therefore, the length of line segment LN is 64 units.