Understanding Inequalities and Their Properties

The video tutorial covers properties and justifying inequalities, similar to properties of equalities. It explains addition, subtraction, multiplication, and division properties of inequalities, highlighting special cases when multiplying or dividing by negative numbers. Two examples are provided to demonstrate solving inequalities using these properties, including the use of the distributive property.

What is the main focus of the lesson on inequalities?

• Properties and justifying inequalities

• Solving quadratic equations

• Graphing linear equations

• Properties of equalities

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

• The inequality reverses

• The inequality remains the same

• The inequality becomes an equality

• The inequality becomes invalid

Which property states that subtracting the same number from both sides of an inequality keeps the inequality unchanged?

• Division property of inequality

• Addition property of inequality

• Subtraction property of inequality

• Multiplication property of inequality

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

• The inequality sign stays the same

• The inequality sign reverses

• The inequality becomes invalid

• The inequality becomes an equality

In the example 7 < 3x - 8, what is the first step to solve the inequality?

• Add 8 to both sides

• Multiply both sides by 3

• Divide both sides by 3

• Subtract 8 from both sides

When solving 7 < 3x - 8, why don't we flip the inequality sign when dividing by 3?

• Because 3 is a negative number

• Because 3 is a prime number

• Because 3 is an even number

• Because 3 is a positive number

In the inequality -5(x - 3) ≤ -20, what is the first step to simplify the expression?

• Divide both sides by -5

• Subtract 5 from both sides

• Add 5 to both sides

• Distribute -5 across the parentheses

After distributing in -5(x - 3) ≤ -20, what is the next step?

• Add 15 to both sides

• Subtract 15 from both sides

• Divide both sides by 5

• Multiply both sides by 5

Why do we flip the inequality sign when dividing both sides by -5 in the example -5(x - 3) ≤ -20?

• Because -5 is a positive number

• Because -5 is a negative number

• Because -5 is an even number

• Because -5 is a prime number