How do you solve and write the following in interval notation: # |1 + 5x| > 11#?

1 Answer
Jim G.
Mar 17, 2017

#(-oo,-12/5)uu(2,+oo)#

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)#

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