SOLUTION: The length of a spring is given by L= 3/4 F + 8, where F is the applied force. What force will produce a 10. I believe the answer will have to be a decimal. Thank you.

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: The length of a spring is given by L= 3/4 F + 8, where F is the applied force. What force will produce a 10. I believe the answer will have to be a decimal. Thank you.      Log On

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Question 93210: The length of a spring is given by L= 3/4 F + 8, where F is the applied force. What force will produce a 10. I believe the answer will have to be a decimal. Thank you.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
L=%283%2F4%29F%2B8 Start with the given equation


10=%283%2F4%29F%2B8 Plug in L=10


%284%29%2810%29=%284%29%28%283%2F4%29F%2B8%29 Multiply both sides by the LCM of 4. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



40=3F%2B32 Distribute and multiply 4 by each term on both sides


0=3F%2B32-40 Subtract 40 from both sides


-3F=32-40 Subtract 3F from both sides




-3+F=-8 Combine like terms -40 and 32 on the right side to get -8





F=%28-8%29%2F%28-3%29 Now divide both sides by -3 to isolate and solve for F


F=+8+%2F+3 Reduce



So the approximate answer is

F=2.66666666666667

which rounds to

F=2.667

So the force needed is about F=2.667