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

2 Answers
Lucio Falabella
Oct 5, 2016

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]}

Alan P.
Oct 5, 2016

(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") :}

Related questions
See all questions in Sign Charts
Impact of this question
4163 views around the world
You can reuse this answer
Creative Commons License