Solve each of the following in equations and represent the solution set on the number line. x-3/x+4<0, x ∈ R

Question

 Solve each of the following in equations and represent the solution set on the number line.

\(\frac{{\text{x}}-3}{{\text{x}} + 4} < 0 , x \in R\)

Answer 1

Given:

\(\cfrac{{\text{x}}-3}{{\text{x}} + 4} < 0 , x \in R\)

Signs of x – 3

x – 3 = 0 → x =3 (Adding both the sides by 3) 

x – 3 < 0 → x < 3 (Adding both the sides by 3) 

x – 3 > 0 → x > 3 (Adding both the sides by 3) 

Signs of x + 4 

x + 4 = 0 → x = -4 (Subtracting both the sides by 4) 

x + 4 < 0 → x < -4 (Subtracting both the sides by 4) 

x + 4 > 0 → x > -4 (Subtracting both the sides by 4)

\(\cfrac{{\text{x}}-3}{{\text{x}} + 4}\) is not defined when x = -4

The interval that satisfies the condition that \(\cfrac{{\text{x}}-3}{{\text{x}} + 4}\)<0 is -4<x<3

Therefore,

x ϵ (-4, 3)