How do you solve #(5-x)^2(x-13/2)<0#? Precalculus Solving Rational Inequalities Polynomial Inequalities 1 Answer Ratnaker Mehta Jul 6, 2016 # x in (-oo,13/2)-{5}# Explanation: Observe that # AAx in RR, (5-x)^2>=0,# equality holds # iff x=5.# Hence, #(5-x)^2(x-13/2)<0 iff (x-13/2)<0 & x!=5 iff x<13/2, x!=5#. This can be put as # x in (-oo,13/2)-{5}# Answer link Related questions What are common mistakes students make when solving polynomial inequalities? How do I solve a polynomial inequality? How do I solve the polynomial inequality #-2(m-3)<5(m+1)-12#? How do I solve the polynomial inequality #-6<=2(x-5)<7#? How do I solve the polynomial inequality #1<2x+3<11#? How do I solve the polynomial inequality #-12<-2(x+1)<=18#? How do you solve the inequality #6x^2-5x>6#? How do you solve #x^2 - 4x - 21<=0# A) [-3, 7] B) (-∞, -3] C) (-∞, -3] [7, ∞) D) [7, ∞)? How do you solve quadratic inequality, graph, and write in interval notation #x^2 - 8x + 15 >0#? How do you solve #-x^2 - x + 6 < 0#? See all questions in Polynomial Inequalities Impact of this question 1181 views around the world You can reuse this answer Creative Commons License