Solving Inequalities Through Multiplication and Division

The lesson covers solving inequalities using multiplication and division, starting with a real-world example involving astronaut weights. It explains how inequalities remain true when both sides are multiplied or divided by positive numbers. The lesson then introduces the concept of reversing the inequality sign when dealing with negative numbers. Guided examples are provided to reinforce these concepts, and the lesson concludes with an application problem involving work hours and earnings.

If an astronaut weighs 300 pounds on Earth and 50 pounds on the Moon, what would be the astronaut's weight on the Moon if their weight is halved?

• 25 pounds

• 75 pounds

• 100 pounds

• 150 pounds

What is the weight of five astronauts on Earth if one astronaut weighs 300 pounds?

• 796 pounds

• 1500 pounds

• 335 pounds

• 3980 pounds

Which property states that an inequality remains true when you multiply or divide each side by a positive number?

• Multiplication Property of Inequality

• Division Property of Inequality

• Subtraction Property of Inequality

• Addition Property of Inequality

Solve the inequality: 8x ≤ 40. What is the value of x?

• x ≥ 8

• x ≤ 5

• x ≥ 5

• x ≤ 8

If d/2 > 7, what is the value of d?

• d > 7

• d < 7

• d < 14

• d > 14

What happens to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?

• It reverses

• It disappears

• It remains the same

• It becomes an equal sign

Solve the inequality: -2g < 10. What is the value of g?

• g > 5

• g < 5

• g > -5

• g < -5

If k/-2 < 9, what is the value of k?

• k > 18

• k < 18

• k > -18

• k < -18

Ling earns $8 per hour. Write an inequality to find how many hours she must work to earn at least $120.

• 8x ≤ 120

• 8x < 120

• 8x > 120

• 8x ≥ 120

If Ling needs to work at least 15 hours to earn $120, what is the minimum number of hours she must work?

• 20 hours

• 15 hours

• 12 hours

• 10 hours