Answer:
The length of LO is 33 inches.
Step-by-step explanation:
Given that M is between L and O, we have the following lengths:
LM = 7x - 9
MO = 14 inches
LO = 10x - 7
Since L-M-O forms a straight line, the sum of the lengths of LM and MO should be equal to the length of LO:
LM + MO = LO
Substitute the given values:
(7x - 9) + 14 = 10x - 7
Now, solve for x:
7x - 9 + 14 = 10x - 7
7x + 5 = 10x - 7
Subtract 7x from both sides:
5 = 3x - 7
Add 7 to both sides:
12 = 3x
Divide by 3:
x = 4
Now that we have the value of x, we can find the length of LO:
LO = 10x - 7
LO = 10(4) - 7
LO = 40 - 7
LO = 33 inches
The length of LO is 33 inches.