Point L is on line segment K M. Given LM = 3x + 3, KM = 5x + 4, and
KL = 5x + 1, determine the numerical length of K M.
To find the length of KM, we need to subtract the length of KL from the length of LM.
LM = KL + KM
3x + 3 = (5x + 1) + (5x + 4)
3x + 3 = 10x + 5
3 = 7x + 5
7x = -2
x = -2/7
Now we can substitute this value of x into the expression for KM to find its length:
KM = 5(-2/7) + 4
KM = -10/7 + 4
KM = -10/7 + 28/7
KM = 18/7
So the numerical length of KM is 18/7.
To determine the numerical length of KM, we need to find the value of x.
We have the equations:
LM = 3x + 3
KM = 5x + 4
KL = 5x + 1
Since point L is on line segment KM, the sum of the lengths of KL and LM should be equal to the length of KM.
So, we can set up the equation:
KL + LM = KM
Substituting the given expressions, we have:
(5x + 1) + (3x + 3) = 5x + 4
Let's solve this equation to find the value of x:
5x + 1 + 3x + 3 = 5x + 4
8x + 4 = 5x + 4
Subtracting 5x from both sides:
8x - 5x + 4 = 5x - 5x + 4
3x + 4 = 4
Subtracting 4 from both sides:
3x + 4 - 4 = 4 - 4
3x = 0
Dividing both sides by 3:
3x / 3 = 0 / 3
x = 0
Therefore, the value of x is 0.
Now, to find the numerical length of KM, we can substitute x = 0 into the equation KM = 5x + 4:
KM = 5(0) + 4
KM = 4
Thus, the numerical length of KM is 4.
To determine the numerical length of K M, we need to find the value of x that satisfies the given conditions.
We have the lengths of LM, KM, and KL:
LM = 3x + 3
KM = 5x + 4
KL = 5x + 1
We know that point L lies on line segment KM, which means the combined lengths of KL and LM should equal the length of KM. Therefore, we can set up the equation:
KL + LM = KM
Substituting the given values:
(5x + 1) + (3x + 3) = 5x + 4
Now, let's simplify the equation:
8x + 4 = 5x + 4
Subtracting 5x from both sides:
3x + 4 = 4
Subtracting 4 from both sides:
3x = 0
Dividing by 3:
x = 0
Now that we have the value of x, we can substitute it back into the expression for KM to find the numerical length of KM:
KM = 5x + 4
KM = 5(0) + 4
KM = 0 + 4
KM = 4
Therefore, the numerical length of K M is 4 units.