Understanding Inequalities and Their Graphs

This lesson covers solving inequalities involving addition and subtraction using properties of equality and inequality. It explains how to graph inequalities on a number line, using open and closed circles to indicate whether numbers are included. The lesson also provides tips for checking solutions and introduces a trick for determining the direction of shading on a graph. The session concludes with a preview of the next lesson, which will focus on inequalities involving multiplication and division.

What is the main focus of lesson 7.1b?

• Solving inequalities involving addition and subtraction

• Understanding complex numbers

• Graphing linear equations

• Solving equations using multiplication

Which of the following is a rational number?

• 3/4

• π

• √2

• e

What does the addition property of equality allow you to do?

• Subtract different numbers from each side of an equation

• Divide both sides of an equation by the same number

• Add the same number to both sides of an equation

• Multiply both sides of an equation by the same number

What happens when you subtract the same number from both sides of an inequality?

• The inequality becomes false

• The inequality reverses direction

• The inequality remains true

• The inequality becomes an equation

What does an open circle on a number line indicate?

• The inequality is false

• The inequality is true

• The number is not included

• The number is included

If x is greater than or equal to -1, how is it represented on a number line?

• Closed circle at -1, arrow to the left

• Open circle at -1, arrow to the right

• Closed circle at -1, arrow to the right

• Open circle at -1, arrow to the left

How can you verify the solution of an inequality?

• By checking the solution with a calculator

• By graphing the inequality

• By solving a different inequality

• By substituting a value from the solution set into the original inequality

What is the trick for graphing inequalities when the variable is on the left?

• The inequality symbol points in the direction of the shading

• The inequality symbol points opposite to the shading

• The variable must be on the right

• The inequality must be an equation

What should you do if the variable is on the right side of the inequality?

• Leave it as is

• Reverse the entire inequality

• Add a constant to both sides

• Subtract a constant from both sides