Rational Inequalities

Two hoses are filling a pool. The first hose fills at a rate of x gallons per minute. The second hose fills at a rate of 15 gallons per minute less than the first hose. To meet the pool maintenance company's schedule, the pool needs to fill at a combined rate of at least 10 gallons per minute. The inequality represents the combined rates of the hoses: 1/x+1/x-15_>1/10 Which answer choice includes all solutions to the inequality and identifies which interval(s) contain viable filling rates for the hoses?

(0,5] U (15,30]; only (15,30] contains viable rates for the hoses

What is the solution of 1/x+1/3<1/5?

-15/2<x<0

Which graph shows the solution set of x-9/7x+2_<0?

C

Which graph shows the solution set of x^2+9x-22/x+4_>0?

C

Which graph shows the solution set of x-1/x-3<0?

D

Which shows all the critical points for the inequality x^2-4/x^2-5x+6<0?

x = -2, x = 2, and x = 3

The critical points of a rational inequality are x = -4 and x = 2. Which set of points can be tested to find a complete solution to the inequality?

x = -5, x = 0, and x = 3

Which shows all the critical points for the inequality 2x+5/x-2_>x-1/x-2?

x = -6 and x = 2

Which shows all the critical points for the inequality x^2-9x/x-5<0?

x = 0, x = 5, and x = 9

What is the solution of x+8/5x-1>0?

x<-8 or x>1/5