A Simple Problem to Find Value of x

Topic : Solve for x

Question : Solve (x-7)(x+5) > 0

Solution :
The product is greater than 0 implies that either both (x-7) and (x+5) are positive or both are negative

because + X + = +
and - X - = +

1) x - 7 > 0
add 7 on both side
so x>7
and x+5 <>
to this add -5 on both side
x < -5
So x >7 and x < -5 implies x>7

2)x - 7 > 0
add 7 on both side
so x>7
and x+5 < 0
to this add -5 on both side
x < -5
So x <7>
Thus we got x>7, x < -5
In interval rotation, it will be (-∞,-5) U (7,∞)