Solving Linear Inequalities: Key Concepts and Techniques

This video tutorial by Kirk Weiler from eMath Instruction covers solving linear inequalities. It begins with an introduction to the topic, followed by a detailed explanation of the properties of inequalities and their similarities to equalities. The tutorial includes exercises demonstrating basic operations and highlights an important exception when multiplying or dividing by negative numbers. It provides a step-by-step guide to solving linear inequalities and instructions on graphing their solutions. The video concludes with a section on simplifying inequalities using properties of numbers.

What is the main focus of this lesson?

• Solving linear inequalities

• Solving quadratic equations

• Understanding functions

• Graphing linear equations

If you add the same number to both sides of a true inequality, what happens?

• The inequality sign changes direction

• The inequality becomes an equation

• The inequality remains true

• The inequality becomes false

What happens to an inequality when you multiply both sides by a negative number?

• The inequality becomes an equation

• The inequality becomes false

• The inequality sign changes direction

• The inequality remains true

Which of the following is true if you subtract the same number from both sides of a true inequality?

• The inequality remains true

• The inequality becomes an equation

• The inequality becomes false

• The inequality sign changes direction

What is the solution to the inequality 4x - 3 ≥ 5?

• x ≥ 2

• x < 2

• x ≤ 2

• x > 2

Which of the following numbers is a solution to the inequality x ≥ 2?

• 1

• 0

• 2

• -1

When solving the inequality 8 - 2x > 16, what is the correct solution?

• x > -4

• x < -4

• x > 4

• x < 4

What should you do when you divide both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Change the inequality sign

• Keep the inequality sign the same

How do you graph the solution set for x < -4?

• Solid dot on -4 and shade to the right

• Open circle on -4 and shade to the right

• Open circle on -4 and shade to the left

• Solid dot on -4 and shade to the left

What is the first step in simplifying the inequality 8(x - 2) - 3(2x + 1) ≤ 7x - 3(x + 1)?

• Combine like terms

• Divide by 2

• Distribute the multiplication

• Add 3 to both sides