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Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?

x < -5

x > -5

x < -1

x > -1

Verified Answer :

let us say, the number is "a"

one less than "a" is ... well a - 1
2/5 of that will be... well, 2/5 ( a - 1)

one more than "a" is... well a + 1
3/5 of that is.. hmmm 3/5 (a + 1)

now, we're told that, the first expression is "less than" the second one, thus

\(\bf \cfrac{2}{5}(a-1)\ \textless \ \cfrac{3}{5}(a+1)\)

solve for "a", or make it "x" if you wish, same thing anyway

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