Solve нства (x + 2)(x - 7) > 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

$$( x + 2 ) ( x - 7 ) \gt 0$$

Solve for x

$x\in \left(-\infty,-2\right)\cup \left(7,\infty\right)$

Solution Steps

For the product to be positive, $x+2$ and $x-7$ have to be both negative or both positive. Consider the case when $x+2$ and $x-7$ are both negative.

$$x+2<0$$ $$x-7<0$$

The solution satisfying both inequalities is $x<-2$.

$$x<-2$$

Consider the case when $x+2$ and $x-7$ are both positive.

$$x-7>0$$ $$x+2>0$$

The solution satisfying both inequalities is $x>7$.

$$x>7$$

The final solution is the union of the obtained solutions.

$$x<-2\text{; }x>7$$