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.