Solving Inequalities with Variables

This video tutorial teaches how to solve inequalities using inverse operations. It begins with a review of key concepts such as variables and solution sets, and highlights common mistakes like using incorrect inverse operations. The core lesson involves a practical example where Debbie has a budget for clothes, and the video demonstrates how to set up and solve an inequality to determine how many t-shirts she can buy. The tutorial concludes by reinforcing the method of solving inequalities similarly to equations, emphasizing the use of inverse operations.

What is the primary method used to solve inequalities in this lesson?

• Graphical representation

• Inverse operations

• Trial and error

• Substitution method

What does a variable represent in an inequality?

• An unknown number or set of numbers

• A fixed number

• A constant value

• A mathematical operation

Which symbols are used when a value is part of the solution set?

• Greater than or equal to or less than or equal to

• Not equal to

• Equal to

• Greater than or less than

What is a common mistake when solving inequalities?

• Using the correct symbols

• Ignoring the variable

• Solving for the wrong variable

• Applying inverse operations incorrectly

What is Debbie's budget for clothes?

• $50

• $60

• $70

• $80

How much does each t-shirt cost in Debbie's example?

• $5

• $12

• $8

• $10

What is the inequality set up to determine the number of t-shirts Debbie can buy?

• 22 + 8x > 60

• 22 + 8x < 60

• 22 + 8x = 60

• 22 + 8x ≤ 60

What is the first step in solving the inequality 22 + 8x ≤ 60?

• Divide both sides by 8

• Multiply both sides by 8

• Subtract 22 from both sides

• Add 22 to both sides

After isolating 8x, what is the next step to solve for x?

• Add 8 to both sides

• Subtract 8 from both sides

• Multiply both sides by 8

• Divide both sides by 8

How many t-shirts can Debbie buy according to the solution?

• 4

• 6

• 5

• 3