Most regular airlines won't check the size, unless it's obviously way larger or heavier than your allowance, but you may need to consider where is that extra inch, if it's too wide/thick, it may not fit in the baggage overhead compartment and a flight attendant may check it in for you…
Can a carry-on be 22.5 inches?
The combined dimensions of carry-on baggage should be less than 45 inches, with individual items measuring no more than 22 x 14 x 9 inches. Delta Connection passengers, including on flights with 50 seats or fewer, are only permitted personal items due to limited overhead space.