How to solve (x-1)/(x+1) >= 1

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-1)/(x+1) >= 1 | Equatix

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Question

$$\frac{ x-1 }{ x+1 } \geq 1$$

Solve for x

$x<-1$

Solution Steps

Denominator $x+1$ cannot be zero since division by zero is not defined. There are two cases.

$$x+1>0$$ $$x+1<0$$

Consider the case when $x+1$ is positive. Move $1$ to the right hand side.

$$x>-1$$

The initial inequality does not change the direction when multiplied by $x+1$ for $x+1>0$.

$$x-1\geq x+1$$

Move the terms containing $x$ to the left hand side and all other terms to the right hand side.

$$x-x\geq 1+1$$

Combine like terms.

$$0\geq 2$$

Consider condition $x>-1$ specified above.

$$x\in \emptyset$$

Now consider the case when $x+1$ is negative. Move $1$ to the right hand side.

$$x<-1$$

The initial inequality changes the direction when multiplied by $x+1$ for $x+1<0$.

$$x-1\leq x+1$$

Move the terms containing $x$ to the left hand side and all other terms to the right hand side.

$$x-x\leq 1+1$$

Combine like terms.

$$0\leq 2$$

Consider condition $x<-1$ specified above.

$$x<-1$$

The final solution is the union of the obtained solutions.

$$x<-1$$

Show Solution

Basic Math

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Example

Question

Solve for x

Solution Steps