Seven minus ten times a number is no less than twenty - two increased by two times the difference of 2 and five times the number

Question

Define a variable, write an inequality and solve the problem

Answer 1

Let n be the number. 7-10n is "7 minus 10 times the number".

"no less than" is "greater than or equal to" or "≥".

"difference of 2 and 5 times the number" is 2-5n.

"22 increased by twice" this difference is 22+2(2-5n).

Putting it all together:

7-10n≥22+2(2-5n) would seem to be the inequality, but there's a problem because:

7-10n≥22+4-10n, and -10n cancels out leaving 7≥26, that is, 19≤0, which is never true, because 19 is positive.

I suggest that this is either a trick question or the difference of 2 and 5 times the number is 5n-2, so:

7-10n≥22+2(5n-2), 7-10n≥22+10n-4, 7-18≥20n, -11/20≥n, so n≤-11/20.