How do you solve #7/(x+3)<-5#?

1 Answer
Jul 29, 2017

Answer:

#(-22/5,-3)#

Explanation:

#"add 5 to both sides"#

#rArr7/(x+3)+5 < 0#

#"express as a single rational function"#

#(7+5(x+3))/(x+3) < 0#

#rArr(5x+22)/(x+3) < 0#

#"the zeros of the numerator/denominator are"#

#"numerator "x=-22/5," denominator "x=-3#

These indicate where the rational function may change sign.

#"the intervals for consideration are"#

#x < -22/5,color(white)(x)-22/5 < x < -3,color(white)(x)x > -3#

#"consider a "color(blue)"test point "" in each interval"#

#"we want to find where the function is negative"#

#"substitute each test point into the function and consider"#
#"it's sign"#

#color(magenta)"x = - 5"to(-)/(-)tocolor(red)" positive"#

#color(magenta)"x = - 4 "to(+)/(-)tocolor(blue)" negative"#

#color(magenta)"x = 4"to(+)/(+)tocolor(red)" positive"#

#rArr-22/5 < x < -3" or " (-22/5,-3)#