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 area comparison problems using inequalities and graphical representation, focusing on linear and quadratic equations. The video concludes with a summary of how to represent inequalities graphically and solve practical problems.

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

• Ignoring variable coefficients

• Using symbols and number lines

• Applying the same processes as equations

• Considering two-variable inequalities

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 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, which formula represents the area of a rectangle?

• 1/2 base times height

• x times (x - 3)

• x times (x + 3)

• 1/2 (x - 3) times height

What is the inequality form after rearranging 2x - 4 < x^2 - 3x?

• x^2 + 5x + 4 < 0

• x^2 + 5x - 4 < 0

• x^2 - 5x - 4 > 0

• x^2 - 5x + 4 > 0

What are the roots of the equation x^2 - 5x + 4 = 0?

• x = 2 and x = 3

• x = -1 and x = -4

• x = 1 and x = 4

• x = 0 and x = 5

For the inequality x^2 - 5x + 4 > 0, which range of x values is valid?

• x = 1 or x = 4

• x < 0 or x > 5

• x > 1 and x < 4

• x < 1 or x > 4