42,726 views
2 votes
Hello! I need some help with this homework question posted below. Q18

Hello! I need some help with this homework question posted below. Q18-example-1
User Fawn
by
3.3k points

1 Answer

4 votes

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

User CryptoJones
by
3.3k points