Solving Two-Step Inequalities in Depth

This video tutorial covers solving two-step inequalities using algebra tiles, modeling inequalities, and applying them to real-world scenarios. It includes graphing solutions and determining valid solutions through substitution. The tutorial emphasizes understanding and interpreting inequalities in various contexts.

What is the first step in solving the inequality 4D - 3 ≥ 9 using algebra tiles?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 4

• Divide both sides by 4

When using algebra tiles, what does adding three tiles to both sides of the inequality accomplish?

• It eliminates the variable

• It simplifies the inequality

• It balances the equation

• It isolates the variable

In the inequality 2x + 7 > 11, what is the next step after removing 7 tiles from both sides?

• Add 7 to both sides

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 7 from both sides

What is the solution to the inequality 5H - 4 ≥ 11 after isolating the variable?

• H ≥ 2

• H ≥ 3

• H ≥ 4

• H ≥ 5

What does Serena need to do to complete the first 3 miles of a 10-mile run in 45 minutes or less?

• Run at a pace of at least 5 miles per hour

• Run at a pace of at least 4 miles per hour

• Run at a pace of at least 6 miles per hour

• Run at a pace of at least 3 miles per hour

What is Joshua's required pace to complete the first mile of a 5-mile run in ten minutes or less?

• At least 7 miles per hour

• At least 4 miles per hour

• At least 5 miles per hour

• At least 6 miles per hour

How can you determine if a given value makes an inequality true?

• By simplifying the inequality

• By solving the inequality

• By using substitution

• By graphing the inequality

If Harika wants to keep her total purchase under $60, how many gallons of gas can she buy if a car wash costs $12 and gas is $4 per gallon?

• 10 gallons

• 13 gallons

• 12 gallons

• 11 gallons

What is the inequality used to determine the number of gallons Harika can buy?

• 4g - 12 > 60

• 4g + 12 < 60

• 4g + 12 > 60

• 4g - 12 < 60

What does the open circle at 12 on the graph of Harika's inequality represent?

• She can buy less than 12 gallons

• She can buy up to but not including 12 gallons

• She can buy more than 12 gallons

• She can buy exactly 12 gallons