Money supply, Interest Rates, and value of the dollar

From a Kaplan question, it states that when the Fed increases the money supply, interest rates decrease, which decreases the value of the dollar as investors seek higher rates of return outside the US. I understand this, but at the same time, won’t a decrease in interest rates increase the quantity demanded of money as firms borrow more at the lower interest rates? And why does this increase in the quantity demanded of money not increase the value of the dollar?

Nevermind, I figured it out while typing the question, but will give what I think is the answer in case this was confusing anybody else. The increase in the quantity demanded of money does not increase the value of the dollar because the value of the dollar is a function of the basket of goods it can purchase, and if there are more dollars floating around (due to the decreased interest rates and higher demand for money), then each dollar can purchase less goods, implying a decrease in the value of the dollar.

I think my confusion was stemming from quantity demanded/demand distinction. An exogenous increase in the “demand” for money will shift the money demand curve out, which will indeed increase interest rates and the value of the dollar. But an increase in the “quantity demanded” of money due to lower interest rates will not.