How do you solve 7/(x+3)<-5?
1 Answer
Jul 29, 2017
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)
