How do you solve #abs(5x-15)-4>=21#?

1 Answer
Mar 25, 2018

Answer:

#(-oo,-2]uu[8,+oo)#

Explanation:

#"inequalities of the type "|x|>=a#

#"Always have solutions of the form"#

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

#rArr|5x-15|-4>=21#

#"add 4 to both sides"#

#rArr|5x-15|>=25#

#rArr5x-15<=-25" or "5x-15>=25#

#"add 15 to both sides in both inequalities"#

#rArr5x<=-10" or "5x>=40#

#"divide both sides in both inequalities by 5"#

#rArrx <=-2" or "x>=8larrcolor(blue)"solution"#

#(-oo,-2]uu[8,+oo)larrcolor(blue)"in interval notation"#