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in Linear Equations by (15.7k points)

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

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

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1 Answer

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by (15.2k points)

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)

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