Solving and Graphing One-Variable Inequalities

This video tutorial explains how to solve and graph one-variable inequalities. It covers the process of simplifying equations, identifying and isolating variables, and using inverse operations. The tutorial also highlights the differences between solving equations and inequalities, particularly when multiplying or dividing by negative numbers. Additionally, it provides guidance on graphing inequalities, determining open or closed points, and using test points to decide shading on a graph.

What is the first step in solving one variable inequalities?

• Identifying the variable

• Using test points

• Simplifying the inequality

• Graphing the inequality

Which property is used to simplify multi-step inequalities?

• Distributive property

• Associative property

• Identity property

• Commutative property

What should you do after simplifying a multi-step inequality?

• Flip the inequality sign

• Graph the inequality

• Identify the variable and operations

• Use test points

When isolating the variable, which operations should be undone first?

• Multiplication and division

• Exponentiation

• Square roots

• Addition and subtraction

What must you do when multiplying or dividing both sides of an inequality by a negative number?

• Keep the inequality sign the same

• Flip the inequality sign

• Add the same number to both sides

• Subtract the same number from both sides

How do inequalities differ from equations in terms of solutions?

• Inequalities have a single solution

• Inequalities have infinite solutions

• Inequalities have complex solutions

• Inequalities have no solutions

What does a closed point on a number line represent?

• The variable is not included

• The variable is included

• The inequality is strict

• The inequality is non-strict

How can you determine where to shade on a number line for an inequality?

• By using the distributive property

• By guessing

• By using test points

• By flipping the inequality sign

What should you do if you are unsure whether to use an open or closed point?

• Use an open point by default

• Use a closed point by default

• Use test points to determine

• Skip graphing the point

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

• Shading towards the true points

• Using the distributive property

• Simplifying the inequality

• Identifying the variable