Solve each of the following in equations and represent the solution se

1.	Solve each of the following in equations and represent the solution set on the number line.\(\frac{{\text{x}}-3}{{\text{x}} + 1} < 0 , x \in R\)
Answer» Given: \(\cfrac{{\text{x}}-3}{{\text{x}} + 1} < 0 , x \in R\) Signs of x – 3 x – 3 = 0 → x = 0 (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 + 1 x + 1 = 0 → x = -1 (Subtracting both the sides by 1) x + 1 < 0 → x < -1 (Subtracting both the sides by 1) x + 1 > 0 → x > -1 (Subtracting both the sides by 1) \(\cfrac{{\text{x}}-3}{{\text{x}} + 1} \) is not defined when x = -1 The interval that satisfies the condition that \(\cfrac{{\text{x}}-3}{{\text{x}} + 1} \) is -1 <x<3 Therefore x ϵ (-1, 3)

Solve each of the following in equations and represent the solution set on the number line.\(\frac{{\text{x}}-3}{{\text{x}} + 1} < 0 , x \in R\)

Answer»

Given:

\(\cfrac{{\text{x}}-3}{{\text{x}} + 1} < 0 , x \in R\)

Signs of x – 3

x – 3 = 0 → x = 0 (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 + 1

x + 1 = 0 → x = -1 (Subtracting both the sides by 1)

x + 1 < 0 → x < -1 (Subtracting both the sides by 1)

x + 1 > 0 → x > -1 (Subtracting both the sides by 1)

\(\cfrac{{\text{x}}-3}{{\text{x}} + 1} \) is not defined when x = -1

The interval that satisfies the condition that \(\cfrac{{\text{x}}-3}{{\text{x}} + 1} \) is -1 <x<3

Therefore

x ϵ (-1, 3)