To get a chance to win a car, you must guess then number of keys in a jar to within 5 of the actual number. Those who are within this range are given a key to try in the ignition of the car. Suppose there are 587 keys in the jar. Write and solve and equation to determine the highest and lowest guesses that will give contestants a chance to win the car.

Question

myininaya · Answer

so we need to be with in 5 units of 587
so we can have 587+5 and 587-5
or anything in between

so we need x to be btw 587+5 and 587-5
like so
587-5<x<587+5

myininaya · Answer

582<x<592

myininaya · Answer

but it says to write an eqaution that will give the highest and lowest guesses

anonymous · Answer

Thank you so much! I thought that was the answer but i wasnt sure because it said equation and not inequality.

anonymous · Answer

Yeah that is why i didnt think that was right. Maybe i will jst have to write an interval notation with it.

myininaya · Answer

let me think

myininaya · Answer

---|----|-----|-----
  582   587    592

--|----|----|---- <- we can make an equation for this one |x|=5 right?
   -5      0     5            

so lets think about the fist one we are not centered at 0 we are centered at 587

so we have |x-587|=5

myininaya · Answer

the equation to obtain the highest and lowest is |x-587|=5

myininaya · Answer

Check:
|x-587|=5
x-587=5              or      x-587=-5
x=587+5                         x=-5+587
x=592                              x=582

myininaya · Answer

:)

myininaya · Answer

do you have any question?

anonymous · Answer

No. That helped me completely. Thank You so much!