Math Points: Solve the inequality x-5/x+3 < 0?

Question

a. 3 < x < 5

b. –3 < x < 5

c. –5 < x < 3

d. –3 > x > 5

ANSWERS are ABOVE:

Answer 1

x-5/x+3 < 0

x-5/x+3 must be a negetive number. so therearetwo cases:

1. if x-5 is positive x+3 must be negative

2. if x-5 is negative x+3 must be positive.

1. x-5 < 0 and x+3>0 ==> x<5 and x>-3 ==> -3 2. do the same thing but x-5>0 and x+3<0

well i think the second case is difficult, soi solve it, too.

x-5>0 and x+3<0 ==> x>5and x<-3
can u find a number which is greateer than 5 and less than -3 ?
there is no such number
so the first case can only be true. -3

Answer 2

This is a very different solution:
1) consider the function y = (x-5)/(x+3)
2) it has a root x=5 and a discontinuity x= -3
3) study the signal of the function :
a) draw the x-axes and mark the number -3(with a hole) and 5(with a dot)
b) you will obtain something like ------------(-3)----------[5]----------

c) choose a value greater than 5, for example x=10, and evaluate the function y. You will obtain a positive result
d) choose a value between -3 and 5 and do the same, you will obtain a negative result
e) choose a value less than -3 and do the same, you will obtain a positive result
4) Now the draw will be something like
++++++++ -------------- ++++++
---------------(-3)--------------[5]-------
5) The answer is the negative interval, because you are looking for y < 0

6) Finally : -3 < x < 5

Answer 3

Is this your homework?!

Since the answer to x - 5/x + 3 < 0 is, I think, irrational I'll assume you mean

(x-5)/(x+3) < 0

First, you find out where the fraction is negative (either the numerator OR the denomenator is less than zero)

---------> x < 5 OR x < -3 [solve x - 5 < 0, x + 3 < 0]

Since they can't both be negative at the same, of course, or you end up back with a positive, x must be less than 5 but not less than -3.


----------> b) -3 < x < 5

Answer 4

Assuming you meant to put parentheses around (x-5) and (x+3)...

(x-5)/(x+3)<0 when exactly one of the following is true:
a) x-5<0 AND x+3>0
b) x-5>0 AND x+3<0

This means.....
a) x<5 AND x>-3
b) x>5 AND x<-3

Part (a) simplifies to -3
Therefore, the answer is -3

Answer 5

(x-5)/(x+3) <0

the value x-5 has to be -ve and and x+3 is positive

because x-5 positive means x+3 is positive so ans >0 which is not possible.

x-5 <0 means x <5
x+3 >0 means x > -3
so value -3 < x < 5

Answer 6

x-5/x+3 <0
x-5 <0 => x+3>0........x<5...........x>-3...........answer is B
x+3<0 => x-5>0 .........x<-3.........x>5....this is wrong statement

Answer 7

what math points are you referring to that would get me motivated to even look at this problem?