Seven less than the product of twice a number is greater than 5 more an the same number. Which integer satisfies this inequality?

1 Answer
Alan P.
Jan 5, 2017

Any integer #13# or greater

Explanation:

Translating into an algebraic form (using #n# as the number):
Seven less than the product of twice a number is greater than 5 more than the same number.

#rarr#Seven less than #(2xxn)# is greater than #5+n#

#rarr (2n)-7# is greater than #5+n#

#rarr 2n-7 > 5+n#

Subtracting #n# from both sides
then adding #7# to both sides
(note, you can add or subtract any amount to both sides of an inequality while maintaining the inequality)
gives:
#color(white)("XXX")n >12#

So any integer number #13# or greater would satisfy the given requirement.

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