Solve (x - 1)(x + 1) < 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(x-1)(x+1)<0$$

Solve for x

$x\in \left(-1,1\right)$

Solution Steps

For the product to be negative, $x+1$ and $x-1$ have to be of the opposite signs. Consider the case when $x+1$ is positive and $x-1$ is negative.

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

The solution satisfying both inequalities is $x\in \left(-1,1\right)$.

$$x\in \left(-1,1\right)$$

Consider the case when $x-1$ is positive and $x+1$ is negative.

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

This is false for any $x$.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(-1,1\right)$$