Solving Compound Inequalities in Algebra

This video tutorial covers the topic of solving compound inequalities, focusing on both 'and' and 'or' types. It begins with an introduction to the basic concepts and symbols used in inequalities. The tutorial then explains how to differentiate between 'and' and 'or' inequalities, providing examples and methods for solving each type. A practical application involving a dog's diet is used to demonstrate the real-world use of compound inequalities. The video concludes with a summary and encourages students to practice solving similar problems.

What symbols are used to represent inequalities?

• Parentheses, brackets, braces

• Plus, minus, multiply, divide

• Greater than, less than, greater than or equal to, less than or equal to

• Equal to, not equal to

If a number is less than -3 or greater than 2, which word should be used to describe this compound inequality?

• And

• Nor

• But

• Or

How would you write the compound inequality for a number that is greater than or equal to -4 and less than 1?

• -4 ≤ x < 1

• -4 < x ≤ 1

• -4 ≤ x ≤ 1

• -4 < x < 1

What is the term used for compound inequalities that have endpoints on each side and are filled in between?

• And

• Or

• Nor

• But

Solve the inequality: 5x - 7 < 13 or -4x + 3 > 11. What are the solutions?

• x < 4 or x > 2

• x > 4 or x < -2

• x < 4 or x < -2

• x < 4 or x > -2

When solving the inequality -12 ≤ 7x + 9 < 16, what is the first step?

• Divide all sides by 7

• Multiply all sides by 7

• Subtract 9 from all sides

• Add 9 to all sides

What is the solution to the inequality -12 ≤ 7x + 9 < 16?

• -3 ≤ x ≤ 1

• -3 < x ≤ 1

• -3 ≤ x < 1

• -3 < x < 1

Enrique plans a diet for his dog River. If River consumes between 510 and 540 calories each day, and eats 1.5 servings of dog food (320 calories per serving) plus treats (15 calories each), how many treats can River have?

• 4 to 5 treats

• 1 to 3 treats

• 3 to 6 treats

• 2 to 4 treats

What is the inequality representing River's calorie consumption?

• 510 ≤ 1.5(320) + 15x < 540

• 510 < 1.5(320) + 15x < 540

• 510 < 1.5(320) + 15x ≤ 540

• 510 ≤ 1.5(320) + 15x ≤ 540

What is the final step to solve the inequality 510 ≤ 1.5(320) + 15x ≤ 540?

• Multiply all sides by 15

• Divide all sides by 15

• Subtract 15 from all sides

• Add 15 to all sides