Suppose you ride your bike uphill to work at a speed of at least x mph. going downhill on the way home, your speed is 5 mph faster. your average speed to and from work is at least 12 mph. which is the correct inequality to model the situation?

The answer would be 4 mph. 

Let x = rate on the return trip Then, x+8 = rate in the other direction Distance = (Rate)(Time), so Time = (Distance/(Rate) Time to campus + Time from campus = 7/3 So, 7/(x+8) + 7/x = 7/3 Divide both sides by 7:  1/(x+8) + 1/x = 1/3Multiply both sides by the LCD, 3x(x+8), to get3x + 3(x+8) = x(x+8)Simplifying, we have 6x + 24 = x2 + 8x now just combine like terms and simplify.