Understanding Inequalities and Graphing

In this video, Jeff Jacobson explains how to solve inequalities using addition and subtraction. He provides two examples: solving and graphing x - 2.7 < -5 and 13 ≤ x + 14. Additionally, he tackles a word problem involving height requirements for astronauts, demonstrating how to write and solve an inequality to determine how much a person can grow and still qualify as an astronaut.

What is the main difference between solving equations and inequalities?

• Inequalities use a different set of numbers.

• Inequalities involve a different symbol instead of an equal sign.

• Inequalities require a different method of calculation.

• Inequalities cannot be graphed.

In the inequality x - 2.7 < -5, what operation is used to isolate x?

• Division

• Addition

• Multiplication

• Subtraction

What is the solution to the inequality x - 2.7 < -5?

• x < -2.3

• x ≥ -2.3

• x ≤ -2.3

• x > -2.3

When graphing x < -2.3, what type of circle is used on the number line?

• Shaded circle

• Open circle

• Closed circle

• Dotted circle

In the inequality 13 ≤ x + 14, what operation is used to isolate x?

• Multiplication

• Division

• Subtraction

• Addition

What is the solution to the inequality 13 ≤ x + 14?

• x ≥ -1

• x < -1

• x ≤ -1

• x > -1

When graphing x ≥ -1, what type of circle is used on the number line?

• Shaded circle

• Closed circle

• Open circle

• Dotted circle

In the astronaut height problem, what is the maximum height allowed?

• 5.25 feet

• 6.25 feet

• 5.75 feet

• 6.75 feet

How is the height of 5 feet 9 inches converted to feet in the astronaut problem?

• 5.8 feet

• 5.9 feet

• 5.75 feet

• 5.7 feet

What inequality represents the maximum growth allowed for the astronaut?

• G < 0.5

• G ≥ 0.5

• G ≤ 0.5

• G > 0.5