Solving One-Variable Inequalities Using Additive and Multiplicative Inverses

The video tutorial explains 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. Two examples are provided to demonstrate the step-by-step process of solving inequalities, including using the distributive property. The tutorial concludes with a summary of the key concepts learned.

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

• The inequality sign is reversed.

• The inequality sign is removed.

• The inequality sign remains the same.

• The inequality becomes an equation.

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

• Add a positive number to both sides.

• Multiply both sides by a negative number.

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

• Switch the inequality sign.

Why is it important to check the solution in the original inequality?

• To ensure the solution satisfies the original inequality.

• To find a different solution.

• To change the inequality sign.

• To verify the solution is incorrect.

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

• Addition property of inequality.

• Distributive property.

• Multiplicative inverse property.

• Subtraction property of inequality.

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

• x is less than 2.

• x is equal to 2.

• x is not equal to 2.

• x is greater than 2.