How do you solve #9x^2+3x-2>=0#? Precalculus Solving Rational Inequalities Polynomial Inequalities 1 Answer Barney V. Jan 26, 2017 #x=1/3>0# Explanation: #9x^2+3x-2-<0# #:.=(3x-1)(3x+2)=0# #:.3x-1=0# #:.3x=1# #:.x=1/3# sustitute #x=1/3# #:.9(1/3)^2+3(1/3)-2=0# #:.9 xx 1/9+3(1/3)-2=0# #:.9/9+3/3-2=0# #:.1+1-2=0# #3x+2=0# #:.3x=-2# #:.x=-2/3# substitute #x=-2/3# #:.9(-2/3)^2+3(-2/3)-2# #:.9(-4/9)+3(-2/3)-2# #:.-36/9-6/3-2=0# #:.-4-2-2=0# #:.-8=0# an extraneous solution 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 3486 views around the world You can reuse this answer Creative Commons License