How do you solve #abs(5k+4)>=36#?

1 Answer
Nov 24, 2017

Answer:

#(-oo,-8]uu[32/5,+oo)#

Explanation:

#"inequalities of the type "|x|>=a#
#"have solutions of the form "#

#x<=-a" OR "x>=a#

#rArr5k+4<=-36" or "5k+4>=36#

#(1)color(white)(x)5k+4<=-36#

#rArr5k<=-40rArrk<=-8#

#(2)color(white)(x)5k+4>=36#

#rArr5k>=32rArrk>=32/5#

#"the solution can be expressed in interval notation as"#

#(-oo,-8]uu[32/5,+oo)#