Solving Inequalities and Distributive Property

Naomi Andre explains how to solve inequalities involving the distributive property and fractions. The process includes simplifying both sides, gathering Y terms on one side, and solving the inequality by dividing and changing the inequality sign. A practice problem is provided for further understanding.

What is the first step in solving inequalities that involve the distributive property?

• Add numbers to both sides

• Simplify both sides using the distributive property

• Divide both sides by a constant

• Subtract variables from both sides

What does the distributive property allow you to do in an expression?

• Multiply a single term by each term inside parentheses

• Combine like terms

• Subtract variables from both sides

• Add constants to both sides

When simplifying the expression 2(5y - 6), what is the result?

• 10y - 6

• 5y - 12

• 5y - 6

• 10y - 12

What is the result of multiplying 5 by the expression (3y + 6)?

• 5y + 18

• 15y + 6

• 3y + 30

• 15y + 30

What is the result of multiplying 2 by the expression (5y - 6)?

• 10y - 12

• 5y - 6

• 5y - 12

• 10y - 6

After using the distributive property, what should be done next in solving the inequality?

• Add all constants to one side

• Gather all variable terms on one side

• Divide both sides by a constant

• Flip the inequality sign

What is the next step after simplifying both sides of the inequality?

• Add 12 to both sides

• Subtract 15y from both sides

• Divide by 5

• Flip the inequality sign

Why is it important to gather all variable terms on one side of the inequality?

• To ensure the inequality sign remains the same

• To make the inequality more complex

• To simplify the process of solving for the variable

• To eliminate the need for the distributive property

What is the result of adding 12 to both sides of the inequality?

• The variable term on the left becomes 22

• The inequality sign flips

• The constant term on the right becomes 42

• The inequality becomes an equation

What is the result of adding 12 to both sides of the inequality?

• The variable term on the left becomes 22

• The inequality becomes an equation

• The inequality sign flips

• The constant term on the right becomes 42