Inequalities and Linear Functions

The video tutorial by Mr. Wooly covers a review of inequalities, including solving them through various examples. It discusses problems involving fencing, budgeting for sandwiches, maintaining a bank balance, and comparing phone plans. The tutorial emphasizes the importance of understanding inequality symbols and operations, such as addition, subtraction, multiplication, and division, especially when dealing with negative numbers. Students are reminded to adhere to classroom guidelines and prepare for their upcoming test.

Which of the following statements is true about negative numbers compared to positive numbers?

• Negative numbers are greater than positive numbers.

• Negative numbers are equal to positive numbers.

• Negative numbers are less than positive numbers.

• Negative numbers are not comparable to positive numbers.

If you subtract 4 from both sides of the inequality -3 < 1, what is the resulting inequality?

• -7 > -3

• -3 < -7

• -3 > -7

• -7 < -3

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

• The inequality sign disappears.

• The inequality sign becomes an equal sign.

• The inequality sign flips direction.

• The inequality sign remains the same.

Solve the inequality: x + 7 ≤ 21. What is the value of x?

• x > 14

• x < 14

• x ≤ 14

• x ≥ 14

If the length of a rectangle is 9 feet more than its width and the perimeter is at most 114 feet, what is the maximum width?

• 18 feet

• 24 feet

• 27 feet

• 33 feet

Kyle can spend a maximum of $45 on sandwiches and chips. If he already spent $11 on chips, how many sandwiches can he buy if each costs $4.25?

• 10 sandwiches

• 6 sandwiches

• 8 sandwiches

• 12 sandwiches

Noah wants to maintain at least $175 in his account. If he starts with $400 and withdraws $20 weekly, for how many weeks can he withdraw?

• 12 weeks

• 10 weeks

• 9 weeks

• 11 weeks

Which inequality represents the condition where the first phone plan is cheaper than the second plan?

• 0.15m + 23 ≥ 75

• 0.15m + 23 = 75

• 0.15m + 23 < 75

• 0.15m + 23 > 75

For how many minutes is the first phone plan cheaper than the second plan if the first plan costs $0.15 per minute plus a $23 fee?

• 345 minutes

• 347 minutes

• 348 minutes

• 346 minutes

What is the maximum number of minutes you can talk on the first phone plan before it becomes more expensive than the second plan?

• 346 minutes

• 345 minutes

• 347 minutes

• 348 minutes