Question

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

Answer 1

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