Question

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

Answer 1

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.