What does it mean to “isolate the variable” when given an equation or an inequality?

It means to get the variable by itself. Isolating the variable means rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation. Hope this helps.

To isolate a variable is to get a variable all by its self on one side of an equation with all of the other variables on the other side

-x=7y+9

if isolating x, then you'd divide by -1 so that x is standing all alone on the left side of the equation

I hope I explained that clear enough