Inequalities and Their Solutions

The video tutorial teaches seventh graders how to solve two-step inequalities, comparing them to two-step equations. It emphasizes the importance of order in operations and introduces reverse PEMDAS for solving inequalities. The tutorial provides multiple examples, including solving inequalities with negative multiplication and parentheses, and offers practice problems with solutions.

What is the first step in solving a two-step inequality?

• Divide both sides by a constant

• Graph the solution

• Add or subtract to isolate the variable

• Multiply both sides by a constant

When solving the inequality 5x - 4 ≥ 11, what is the value of x?

• x ≤ 3

• x ≥ 2

• x ≥ 3

• x ≤ 2

Why is it important to switch the inequality sign when dividing by a negative number?

• It is not necessary to switch the sign

• It ensures the inequality remains true

• It simplifies the equation

• It is a rule for all equations

In the inequality B / -3 + 4 < 13, what is the solution for B?

• B > -27

• B < -27

• B < 27

• B > 27

Which method can be used to solve the inequality -7(x + 3) ≤ 28?

• Only distribute the -7

• Only divide by -7

• Either distribute the -7 or divide by -7

• Neither method works

How does ordering in bulk affect the price per item?

• Increases the price per item

• Decreases the price per item

• Doubles the price per item

• Has no effect on the price

If a sweatshirt's base price is $40 and the discount is 5 cents per item, what is the maximum number of sweatshirts that can be ordered to keep the price at or below $32.50?

• 100

• 150

• 250

• 200

What is the solution to the inequality 6Y > 12?

• Y < 2

• Y < 1

• Y > 2

• Y > 1

Which of the following inequalities is equivalent to -3d ≥ 15?

• d ≥ 5

• d ≥ -5

• d ≤ 5

• d ≤ -5

What is the correct graphing method for the inequality W/4 > 1?

• Open circle at 1, shade to the left

• Closed circle at 1, shade to the left

• Open circle at 4, shade to the right

• Closed circle at 4, shade to the right