At which x value will f(x)=3x+3 exceed g(x)=3x+10

We write an inequality:







This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination.   is a linear function while is an exponential one (with limit zero as approaches ).  We see that at approximately and .

Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at .  By observing our graph, we see that when or .