I really need help in solving this problem, anyone?

Question

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.

x^2 + 4x + 3 > 0

I need the interval notation expressed in terms of {x| ????}

Answer 1

x² + 4x + 3 > 0

(x + 1)(x + 3) > 0

This is true when
x + 1 > 0 AND x + 3 > 0
OR
x + 1 < 0 AND x + 3 < 0

x > -1 AND x > -3
OR
x < -1 AND x < -3

x > -1
OR
x < -3

The graph will have open circles at -3 & -1 with
shading to the left of -3 and to the right of -1

Interval notation
(-∞ , -3) , (-1, ∞)

Answer 2

x^2 + 4x + 3 >0
(x + 3)(x + 1) >0

Using a table
'x' x<-3 -3-1
x+3 -ve +ve +ve
x+1 -ve -ve +ve
_______________________________
(x+3)(x+1) +ve -ve +ve

So when '-3 < x < -1' the curve is below the 'x' axis.
Otherwise it is above the 'x' axis.
The solutions to 'x' are '-3' and '-1'.
The curve crosses (Intercepts) the y-axis at '+3'.
The minimum point is at:- (-2, 1).