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