Graphing and Solving Inequalities

The video tutorial explains how to solve and graph compound inequalities, focusing on one-step inequalities. It begins by treating inequalities like equations, using inverse operations to solve them. The tutorial then demonstrates how to graph these inequalities on a number line, explaining the difference between open and closed points. It concludes with testing points to determine the correct shading for the solution on the number line.

What is the first step in solving a compound inequality?

• Using a calculator

• Testing points on a number line

• Treating it as an equation

• Graphing the inequality

When solving inequalities, what should you do to isolate the variable?

• Add a constant to both sides

• Use inverse operations

• Multiply both sides by zero

• Ignore the variable

What operation would you use to solve the inequality x + 3 > 7?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 3 from both sides

• Add 3 to both sides

What is the result of solving the inequality x + 3 > 7?

• x > 3

• x > 10

• x > 4

• x > 7

How do you represent a solution on a number line when the inequality is strict (e.g., x > 7)?

• With an open circle

• With a triangle

• With a closed circle

• With a shaded circle

What is the first step in graphing an inequality on a number line?

• Calculating the slope

• Testing all points

• Finding the midpoint

• Drawing the number line

What is the purpose of testing points on a number line?

• To check for symmetry

• To determine the correct shading direction

• To calculate the slope

• To find the midpoint

When should you use a closed circle on a number line?

• When the inequality is strict

• When the inequality includes 'or equal to'

• When the inequality is an equation

• When the inequality is false

What should you do if the inequality is x ≥ 7?

• Use an open circle

• Use a closed circle

• Use a triangle

• Use a dashed line

What does an open circle on a number line indicate?

• The point is included in the solution

• The point is not included in the solution

• The inequality is an equation

• The inequality is false