GCSE Secondary Maths Age 13-17 - Algebra: Inequalities - Explained

The video tutorial explains how to solve the inequality X^2 > 3(X + 6). It begins by expanding the brackets and simplifying the expression to X^2 - 3X - 18 > 0. The instructor then factorizes the quadratic to find key points and uses a graph to determine where the quadratic is positive. The solution is found by identifying the regions where the graph is above the X-axis, leading to the final answer: X > 6 or X < -3. The tutorial emphasizes the importance of correct initial steps and graphical representation for accuracy.

What is the first step in solving the inequality X^2 > 3(X + 6)?

• Factorize the expression

• Find the roots

• Expand the brackets

• Graph the equation

Which factor pair is used to factorize the expression X^2 - 3X - 18?

• 5 and 4

• 6 and 3

• 18 and 1

• 9 and 2

What are the roots of the equation (X - 6)(X + 3) = 0?

• X = 6 and X = -3

• X = 3 and X = -6

• X = 9 and X = -2

• X = 2 and X = -9

In which regions is the quadratic expression X^2 - 3X - 18 greater than zero?

• X > 6 or X < -3

• X < 6 and X > -3

• X > 3 or X < -6

• X < 3 and X > -6

Why is it important to graph the quadratic equation when solving inequalities?

• To check for calculation errors

• To simplify the expression further

• To visualize the regions where the inequality holds

• To find the exact values of X