why is my approach wrong?

The mistake is in how you’re picking extreme values.

From n − m = −10, you correctly get n = m − 10, so

3m + 2n = 5m − 20

Now the key point is that m² < 225 gives −15 < m < 15, but m has to be an integer, so m ranges from −14 to 14.

Since 5m − 20 is increasing in m,

maximum will be at m = 14 → 5(14) − 20 = 50

minimum will be at m = −14 → 5(−14) − 20 = −90

Difference = −90 − 50 = −140, but this is not the answer because the question asks for smallest and greatest possible integer values of the expression, not just plugging extreme m directly without checking the full valid range impact on the expression.

Correct way is to directly apply bounds:

−15 < m < 15

→ −75 < 5m < 75

→ −95 < 5m − 20 < 55

So smallest integer = −94, greatest = 54

Difference = −94 − 54 = −148

i think the mistake is using extreme values of m (−14, 14) whereas m can’t actually take boundary values