Answer:

Solution

Expand the equation;

x2 + 4x – 3xy – 12y = 0

Factorize;

⟹ x (x + 4) – 3y (x + 4) = 0

x + 4) (x – 3y) = 0

⟹ x + 4 = 0 or x – 3y = 0

⟹ x = -4 or x = 3y

Thus, x = -4 or x = 3y

To solve a quadratic inequality, we also apply the same method as illustrated in the procedure below:

Write the quadratic inequality in standard form: ax2 + bx + c where a, b and are coefficients and a ≠ 0

Determine the roots of the inequality.

Write the solution in inequality notation or interval notation.

If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

Example 1

Solve the inequality x2 – 4x > –3

Solution

First, make one side one side of the inequality zero by adding both sides by 3.

x2 – 4x > –3 ⟹ x2 – 4x + 3 > 0

Factor the left side of the inequality.

Step-by-step explanation:

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