Understanding Inequalities and Their Applications

The video tutorial covers solving inequalities using addition and subtraction, similar to solving equations but with inequality signs. It explains the properties of inequalities, such as maintaining truth when adding or subtracting the same number on both sides. The tutorial includes examples of solving inequalities, graphing solutions, and handling word problems. It emphasizes the importance of switching the order of terms for easier graphing and understanding.

What is the main difference between solving equations and solving inequalities?

• Inequalities use a different set of numbers.

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

• Inequalities cannot be graphed.

• Inequalities require multiplication.

What happens when you add the same number to both sides of an inequality?

• The inequality becomes false.

• The inequality sign changes direction.

• The inequality remains true.

• The inequality becomes an equation.

When graphing the inequality X > 4, what type of circle is used at 4?

• Closed circle

• Open circle

• No circle

• Half-filled circle

If an inequality is written as 11 ≥ X, what is the correct way to rewrite it for easier graphing?

• X ≥ 11

• X = 11

• X ≤ 11

• 11 ≤ X

What is the first step in solving the inequality 15 ≥ 6 + X?

• Divide both sides by 6

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by 6

In the inequality 7 ≤ M, what does the inequality indicate about M?

• M is less than 7

• M is greater than or equal to 7

• M is less than or equal to 7

• M is greater than 7

A flea market has more than 250 booths, with 184 filled. How many are still available?

• More than 66

• Exactly 66

• Less than 66

• 250

If you have spent $24 and need to spend at least $75 for free shipping, how much more do you need to spend?

• $100

• $24

• $75

• $51

What is the inequality to represent spending at least $75 for free shipping if $24 is already spent?

• 24 + X ≤ 75

• 24 + X ≥ 75

• 24 + X > 75

• 24 + X < 75

Why might it be worth spending a little extra to get free shipping?

• To receive a gift

• To get a discount on future purchases

• To increase the total purchase

• To avoid paying for shipping