Solving Linear Inequalities: Key Concepts and Techniques

This video tutorial covers the basics of solving linear inequalities, including transforming linear equations into inequalities, testing solutions, and graphing them on a coordinate plane. It provides step-by-step instructions and examples to illustrate the process, including how to handle horizontal and vertical inequalities.

What is a linear inequality in two variables?

• An equation with no variables

• An equation with an equal sign

• An equation with a variable exponent greater than one

• An equation where the equal sign is replaced with an inequality symbol

Which of the following points is a solution to the inequality y > 3x - 7?

• (2, 3)

• (0, 0)

• (4, 1)

• (-1, 5)

What is the first step in graphing a linear inequality?

• Determine if the boundary line is dotted or solid

• Find the slope and y-intercept of the boundary line

• Test a point

• Shade the graph

When should the boundary line be dotted?

• When the inequality is an equation

• When the inequality is 'greater than' or 'less than'

• When the inequality is 'greater than or equal to'

• When the inequality is 'less than or equal to'

In the inequality y > x - 2, what is the slope and y-intercept?

• Slope: 1, y-intercept: (0, -2)

• Slope: -1, y-intercept: (0, 2)

• Slope: 1, y-intercept: (0, 2)

• Slope: 2, y-intercept: (0, -1)

For the inequality y > -3/4x + 2, which point should be tested to determine the shading?

• (3, 3)

• (2, 2)

• (1, 1)

• (0, 0)

What is the boundary line for the inequality y < -2/3x - 1?

• y = 2/3x - 1

• y = -2/3x + 1

• y = 2/3x + 1

• y = -2/3x - 1

How do you determine if a point is a solution to a linear inequality?

• By finding the y-intercept

• By finding the slope

• By graphing the point

• By substituting the point into the inequality and checking if the statement is true

What type of line is x = -1?

• Vertical

• Diagonal

• Curved

• Horizontal

For the inequality y ≥ 2, where should the shading be?

• Above the line

• Below the line

• To the left of the line

• To the right of the line