Representing Inequalities Graphically and Solving Practical Problems

The video tutorial covers a recap of inequalities, including symbols and representation on a number line. It explains how to graph linear equations by identifying gradients and y-intercepts. The tutorial then describes how to use inequalities to define shaded regions on a graph. It also demonstrates solving practical problems by comparing areas of geometric shapes using inequalities. The video concludes with a summary of representing inequalities graphically.

Which of the following is NOT a method used to solve inequalities?

• Graphical representation

• Using logarithms

• Applying the same processes as equations

• Using number lines

What is the equation of a line with a gradient of 2 passing through 4 on the y-axis?

• y = -2x + 4

• y = -2x - 4

• y = 2x - 4

• y = 2x + 4

How do you represent a shaded region below a dashed line with the equation y = 2x + 4?

• y ≤ 2x + 4

• y ≥ 2x + 4

• y < 2x + 4

• y > 2x + 4

In comparing areas, if the area of a triangle is less than that of a rectangle, which inequality represents this?

• Area of triangle < Area of rectangle

• Area of triangle ≥ Area of rectangle

• Area of triangle > Area of rectangle

• Area of triangle = Area of rectangle

What is the factorized form of the quadratic inequality x² - 5x + 4 > 0?

• (x - 2)(x - 3)

• (x + 1)(x + 4)

• (x - 1)(x - 4)

• (x + 2)(x + 3)

Where does the quadratic equation x² - 5x + 4 cross the y-axis?

• At y = 1

• At y = 4

• At y = 5

• At y = 0

For the inequality x² - 5x + 4 > 0, which range of x values is valid?

• x < 0 or x > 5

• x > 1 and x < 4

• x < 1 or x > 4

• x = 1 or x = 4