Inequalities and Linear Equations

The video tutorial covers solving inequalities in various contexts, including concert ticket pricing and sugar reduction in recipes. It explains how to evaluate inequalities, graph solutions on a number line, and create equations from tape diagrams. Additionally, it demonstrates calculating percentage increases, using Claire's height as an example.

What is the correct solution to the inequality 5 - 3x > 35?

• x < -10

• -10 < x

• -10 > x

• x > -10

Why do we change the inequality sign when dividing by a negative number?

• To ensure the inequality remains true

• To maintain the inequality's balance

• To make calculations easier

• Because it is a rule of thumb

What is the expected attendance if the ticket price is $8?

• 650

• 575

• 725

• 600

If the ticket price is $8.50, what is the expected attendance?

• 600

• 725

• 575

• 650

What should the ticket price be to ensure at least 600 attendees?

• $8 or more

• $8 or less

• $7.50 or more

• $9 or more

Which inequality is true when x = -3?

• x - 6 > -3.5

• -x - 6 > -3.5

• -x - 6 > 3.5

• -x - 6 < -3.5

Why is -3 greater than -3.5?

• Because -3 is closer to zero

• Because -3 is a smaller negative number

• Because -3 is further from zero

• Because -3 is a larger negative number

What does the inequality x ≤ 5 represent on a number line?

• An open circle at 5 with an arrow pointing left

• A filled circle at 5 with an arrow pointing right

• A filled circle at 5 with an arrow pointing left

• An open circle at 5 with an arrow pointing right

How is the inequality x < 2.5 represented on a number line?

• A filled circle at 2.5 with an arrow pointing left

• A filled circle at 2.5 with an arrow pointing right

• An open circle at 2.5 with an arrow pointing right

• An open circle at 2.5 with an arrow pointing left

What equation represents the tape diagram with 19 + 7x = 40?

• 19 + 7x = 40

• 7x + 19 = 40

• 40 = 7x + 19

• 40 = 19 + 7x