The inequality is
x^2 + 5x < 6
Subtracting 6 from both sides of the inequality, we have
x^2 + 5x - 6 < 6 - 6
x^2 + 5x - 6 < 0
The expression on the left is a quadratic expression. We would factorise the expression. The first step is to multiply the first and last terms. It becomes
x^2 * - 6 =- 6x^2
Next, we would find two terms such that their sum or difference is 5x and their product is - 6x^2. The terms are 6x and - x. We would replace 5x in the expression with 6x - x. It becomes
x^2 + 6x - x - 6
By factorising, we have
x(x + 6) - 1(x + 6)
Since x + 6 is common, it becomes
(x - 1)(x + 6)
Thus, the expression becomes
(x - 1)(x + 6) < 0
x - 1 < 0 or x + 6 < 0
x < 1 or x < - 6
The solution set in interval notation is (- 6 < x < 1)
The correct graph is A