How do you solve #(x+7)/(x-3)>0# using a sign chart?

2 Answers
Oct 5, 2016

Answer:

# x <-7 vvx>3#

Explanation:

This is a rational inequation where #(P(x))/(Q(x))>0#
Therefore we have to solve:

#P(x)>0#
#Q(x)>0#

And plot the sign chart

#x+7>0=>x > -7#
#x-3>0=>x>3#

enter image source here

Therefroe the follows regions of xy-plot

graph{(x+7)(x-3)>0 [-8.89, 8.885, -4.444, 4.44]}

Oct 5, 2016

Answer:

#(x+7)/(x-3) > 0# for #x < -7# and #x > 3#

Explanation:

Given #(x+7)/(x-3)#

The obvious points of interest will occur when
#color(white)("XXX")x+7= 0 rarr x=-7#
and when
#color(white)("XXX")x-3=0rarr x=3#

This gives us 3 ranges;
for each we can ask if the relation #(x+7)/(x-3) > 0# is true.

Sign chart
#{: ("range: ",x < -7,color(white)("X"),x in (-7,+3),color(white)("X"),x > +3), ("sample value in range: ",-10,,0,,+10), ((x+7)/(x-3)" at sample value: ",+ve,,-ve,,+ve), ((x+7)/(x-3) > 0,"Yes",,"No",,"Yes") :}#