Solving One-Variable Inequalities Using Additive and Multiplicative Inverses

This video tutorial teaches how to solve inequalities using additive and multiplicative inverses. It covers the addition and multiplication properties of inequalities, emphasizing the need to reverse the inequality sign when multiplying by a negative number. The tutorial includes examples to illustrate these concepts, demonstrating step-by-step solutions for different types of inequalities.

What happens to the inequality sign when both sides of an inequality are multiplied by a negative number?

• The inequality sign is doubled.

• The inequality sign is removed.

• The inequality sign is reversed.

• The inequality sign remains the same.

In the example where 3x is greater than 2x plus 7, what is the first step to solve the inequality?

• Multiply both sides by a negative number.

• Add a positive number to both sides.

• Dedicate one side to x's and one side to numbers.

• Reverse the inequality sign.

Why is it unnecessary to reverse the inequality sign in the example where 3x is greater than 2x plus 7?

• Because no negative numbers are involved.

• Because the inequality is already true.

• Because the inequality sign is always reversed.

• Because both sides are equal.

In the example where negative 4 times the quantity x minus 5 is less than 2x plus 8, what property is used first?

• Distributive property.

• Multiplication property of inequality.

• Subtraction property.

• Addition property of inequality.

What is the solution to the inequality after applying the distributive property and reversing the inequality sign in the second example?

• x is equal to 2

• x is greater than 2

• x is less than 2

• x is not equal to 2