Solving Multi-Step Inequalities Challenge

The video tutorial explains how to solve multi-step inequalities by combining knowledge from previous lessons on equations and inequalities. It emphasizes the importance of isolating the variable and using inverse operations, while highlighting the need to switch the inequality symbol when multiplying or dividing by a negative. The tutorial includes an example problem and discusses special cases where no solution or all real numbers are possible.

What is the ultimate goal when solving any inequality?

• To find the value of the variable

• To isolate the variable on one side of the inequality symbol

• To combine like terms

• To apply the distributive property

What is the first step in solving a multi-step inequality?

• Applying inverse operations

• Cleaning up the inequality

• Combining like terms

• Isolating the variable

Which property is used to clean up the inequality?

• Associative property

• Distributive property

• Identity property

• Commutative property

What should you do after cleaning up the inequality?

• Isolate the variable

• Apply the distributive property

• Combine like terms

• Reunite the variables

What must you remember to do when you multiply or divide by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Switch the inequality symbol

• Combine like terms

What happens if the variable terms cancel out and you are left with a false statement?

• There is no solution

• The solution is all real numbers

• The inequality is invalid

• You need to recheck your steps

What is the result if the variable terms cancel out and you are left with a true statement?

• You need to recheck your steps

• There is no solution

• The solution is all real numbers

• The inequality is invalid

In the example, what is the result of solving 4(3n - 1) ≥ 2(n + 3)?

• n ≥ 1

• n ≤ 1

• n ≥ 2

• n ≤ 2

What is the first step in solving the inequality 4(3n - 1) ≥ 2(n + 3)?

• Combine like terms

• Apply the distributive property

• Isolate the variable

• Subtract 2n from both sides

What is the final step in solving the inequality 4(3n - 1) ≥ 2(n + 3)?

• Subtract 2n from both sides

• Add 4 to both sides

• Multiply both sides by 10

• Divide both sides by 10