How do I solve the polynomial inequality #-6<=2(x-5)<7#? Precalculus Solving Rational Inequalities Polynomial Inequalities 1 Answer AltairSafir Apr 21, 2018 #2<=x<17/2# Explanation: (1)#-6<=2(x-5)# and (2)#2(x-5)<7# (1): #-6<=2 x-10# #10-6<=2x# #4<=2x# #2 <=x# (2) #2(x-5)<7# #2 x-10<7# #2 x < 7+10# #2 x <17 # #x<17/2# Result: #2<=x<17/2# 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 #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#? How do you solve #7+13x - 2x^2>0#? See all questions in Polynomial Inequalities Impact of this question 4427 views around the world You can reuse this answer Creative Commons License