Understanding Inequalities from Word Problems

This video tutorial teaches how to create inequalities from word problems using algebraic reasoning. It begins with an introduction to inequalities and a review of key concepts like variables and solutions. The video highlights common mistakes, such as incorrect use of inequality symbols. The core lesson involves solving a word problem where Debbie has a budget to buy clothes, leading to the creation of an inequality. The tutorial outlines steps to identify unknowns, consider multiple solutions, and choose the correct inequality sign. The solution is explained, resulting in the inequality 22 + 8x ≤ 60.

What is an inequality?

• A mathematical statement with no solution

• A mathematical statement with multiple solutions

• A mathematical statement with one solution

• A mathematical statement with only positive solutions

Which symbol is used when the value is not part of the solution set?

• Less than or equal to

• Greater than or equal to

• Greater than or less than

• Equal to

What does a variable represent in an equation?

• A fixed symbol

• An unknown number or set of numbers

• A constant value

• A known number

What is the maximum amount Debbie can spend on clothes?

• $50

• $80

• $60

• $70

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

• $5

• $8

• $12

• $10

What is the first step in writing an inequality from a word problem?

• Determine the solution set

• Identify the unknowns and represent them with variables

• Solve the equation

• Calculate the total cost

What is the constant in the inequality for Debbie's problem?

• The cost of t-shirts

• The cost of jeans

• The total budget

• The number of t-shirts

Why is an inequality used instead of an equation in Debbie's problem?

• Because the budget is fixed

• Because the total cost can vary

• Because there is only one solution

• Because the cost of jeans is unknown

What inequality symbol is used in Debbie's problem?

• Less than

• Less than or equal to

• Greater than

• Equal to

What is the final inequality representing Debbie's spending?

• 22 + 8x = 60

• 22 + 8x ≤ 60

• 22 + 8x > 60

• 22 + 8x < 60