There are two ways to solve this:
Method 1. You can add d to both sides, since you are subtracting d. This is pretty quick, but it can be confusing because normally you add, subtract, etc. numbers, not variables.
Method 2. You can subtract 38 from both sides (because 38-d=-d+38), then divide by -1. This takes a while, plus you have to flip the inequality symbol, turning the > into a <. However, you only have to use numbers--you don't add, subtract, etc. the variable.
Both methods give the same answer; it's a matter of preference. I will do both.
Method 1:
38-d<37
Add d to both sides.
38<37+d
Subtract 37 from both sides (see footnote):
38-37>d
Simplify:
1>d, which can be rewritten as d>1.
Therefore, d>1.
Method 2:
38-d<37
Subtract 38 from both sides:
-d<-1
Divide by -1 and flip the <, making it a > (you can see why: 1<2, divide by -1 and you get -1<-2 -- whoops! Turn the < into a > and everything's fine.):
d>1
Therefore, d>1.
Let's check. Since 3>1, we can substitute 3 for d:
38-3<37
35<37
We're good!
So, the solution is d>1.
Footnote: 37+d=d+37 by the Commutative Property of Addition, so you subtract to cancel out the addition. (I put this separately to stop the paragraph from being too long.)
