Understanding Inequalities and Their Applications

This video tutorial by Mr. E covers lesson 7.1 on writing and solving one-step inequalities. It begins with an introduction to inequalities, followed by solving practice problems and word problems. The video emphasizes the importance of reversing the inequality sign when multiplying or dividing by a negative number. It also includes additional examples to reinforce understanding.

What is the primary focus of one-step inequalities?

• Solving inequalities using one operation

• Graphing complex functions

• Finding the exact value of variables

• Solving equations with two variables

When adding or subtracting a number to both sides of an inequality, what happens to the inequality?

• The inequality sign reverses

• The inequality becomes false

• The truthfulness remains unchanged

• It becomes an equation

What must you do when multiplying or dividing both sides of an inequality by a negative number?

• Subtract a constant from both sides

• Reverse the inequality sign

• Multiply by a positive number

• Add a constant to both sides

In the context of inequalities, what does 'at most' mean?

• Greater than

• Less than or equal to

• Equal to

• Greater than or equal to

If a physicist wants to ensure a metal does not get colder than -80 degrees Celsius, which inequality represents this condition?

• Temperature < -80

• Temperature > -80

• Temperature ≤ -80

• Temperature ≥ -80

What is the solution to the inequality 6s ≤ 42?

• s ≤ 7

• s > 7

• s ≥ 7

• s = 7

If Tom needs to spend $50 or more to get a free meal and has already spent $30.25, how much more does he need to spend?

• $21.00

• $18.75

• $20.00

• $19.75

What is the greatest amount of spinach Selena can buy if she has $10 and spinach costs $3 per pound?

• 3.5 pounds

• 3.33 pounds

• 4 pounds

• 3 pounds

If Florence wants to spend no more than $3 on onions priced at $1.25 per pound, can she buy 2.5 pounds?

• Yes, because it costs exactly $3

• No, because it costs exactly $3

• Yes, because it costs less than $3

• No, because it costs more than $3

What does 'no more than' imply in terms of inequalities?

• Equal to

• Less than or equal to

• Less than

• Greater than