How do you solve and write the following in interval notation: # |1 + 5x| > 11#?
1 Answer
Mar 17, 2017
Explanation:
To solve inequalities of this type, we have to solve 2 inequalities.
#|x|>a" then " x< color(red)(-a)" or " x > color(red)(a)#
#rArr1+5x< color(red)(-11)" or " 1+5x > color(red)(11)#
#color(blue)"solve " 1+5x<-11# subtract 1 from both sides.
#cancel(1)cancel(-1)+5x< -11-1#
#rArr5x<-12# divide both sides by 5
#(cancel(5) x)/cancel(5)<(-12)/5#
#rArrx<-12/5larrcolor(red)"first solution"#
#color(blue)"solve " 1+5x>11#
#rArr5x>10#
#rArrx>2larrcolor(red)" second solution"#
#"Expressing the solution in interval notation"#
#(-oo,-12/5)uu (2,+oo)#
