Question 148572
Let x=score on sixth exam


So the average A of all 6 exams are



{{{A=(84+86+71+91+98+x)/6}}}



Since the average must be greater than or equal to 82, this means that the right side is greater than or equal to 82


{{{(84+86+71+91+98+x)/6>=82}}} Set the right side greater than or equal to 82



{{{84+86+71+91+98+x>=492}}} Multiply both sides by 6.



{{{x+430>=492}}} Combine like terms on the left side.



{{{x>=492-430}}} Subtract {{{430}}} from both sides.



{{{x>=62}}} Combine like terms on the right side.



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Answer:


So the answer is {{{x>=62}}} which means that the student must get a 62 or better on the 6th exam in order to get an overall average grade of 82 or better.