Solving Multi-Step Inequalities with the Distributive Property

The video tutorial explains how to solve multi-step inequalities using the distributive property. It begins with setting up the problem, then demonstrates swapping sides to keep the variable on the left. The tutorial continues by applying the distributive property and solving the inequality step-by-step. Finally, it shows how to graph the solution on a number line, explaining the significance of open and closed circles.

What is the first step in solving multi-step inequalities with the distributive property?

• Graphing the solution

• Isolating the variable

• Distributing the number across the terms

• Swapping sides of the inequality

Why do we swap sides of the inequality in the given problem?

• To avoid negative numbers

• To make the equation simpler

• To keep the variable on the left-hand side

• To change the order of terms

What should you ensure when swapping sides of the inequality?

• Keep the sign open towards the same number

• Add a constant to both sides

• Flip the inequality sign

• Change the order of terms

What is the result of distributing -3 across the terms inside the parentheses (n + 2)?

• 3n + 6

• -3n + 6

• -3n - 6

• 3n - 6

What is the next step after distributing the negative number?

• Graphing the solution

• Multiplying both sides by a constant

• Adding the opposite of the constant term

• Swapping sides again

What is the unique rule when dividing or multiplying by a negative number in inequalities?

• Add a constant to both sides

• Flip the inequality sign

• Subtract a constant from both sides

• Keep the inequality sign the same

What is the final solution of the inequality after solving it?

• n < 10

• n > 10

• n < -10

• n > -10

What type of circle is used to represent the solution on the number line when the inequality is 'greater than'?

• Open circle

• No circle

• Half-filled circle

• Closed circle

What does an open circle on the number line indicate?

• The number is a solution

• The inequality is 'less than or equal to'

• The number is not a solution

• The inequality is 'greater than or equal to'

Why is it helpful to keep the variable on the left-hand side when solving inequalities?

• To avoid negative numbers

• To make the equation simpler

• To easily graph the solution

• To change the order of terms