Solving Multi-Step Inequalities Effectively

This video tutorial covers solving inequalities using addition, subtraction, multiplication, and division. It explains how to handle special cases like no solution and all real numbers. The tutorial also includes a real-world problem involving a runner's average time, demonstrating how to apply inequalities in practical scenarios. Key concepts include the importance of flipping the inequality sign when multiplying or dividing by a negative number and using distribution to simplify expressions.

What is the first step in solving the inequality p/8 > 4?

• Divide both sides by 8

• Multiply both sides by 8

• Subtract 9 from both sides

• Add 9 to both sides

When multiplying or dividing both sides of an inequality by a negative number, what must you remember to do?

• Keep the inequality sign the same

• Subtract the same number from both sides

• Flip the inequality sign

• Add the same number to both sides

What is the result of distributing 6a in the inequality 6a - 2 > 18?

• 6a - 2

• 6a + 2

• 12a - 2

• 12a + 2

In the inequality -6a ≤ 18, what happens to the inequality sign when you divide both sides by -6?

• It stays the same

• It disappears

• It flips

• It becomes an equal sign

How do you handle an inequality with variables on both sides, such as 4 - 2m > 3m + 7?

• Subtract the variables from one side

• Add the variables to one side

• Divide both sides by the variable

• Combine like terms

When solving the inequality m + 4 > 7, what is the next step after combining like terms?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 4 from both sides

• Add 4 to both sides

What is the solution to the inequality -4 ≤ -3 after canceling out the variables?

• No solution

• All real numbers

• x > 0

• x < 0

In the inequality 2x - 8 > 2x - 6, what is the result after subtracting 2x from both sides?

• -8 > -6

• -8 < -6

• 0 > 0

• 0 < 0

What is the first step in solving the inequality for the runner's average time?

• Add all race times together

• Multiply by the number of races

• Divide by the number of races

• Subtract the slowest time

If a runner wants an average time of less than 24 minutes, what must their next race time be?

• Exactly 24 minutes

• Less than 21.9 minutes

• More than 21.9 minutes

• More than 24 minutes