Understanding Inequalities and Their Solutions

This video tutorial teaches how to solve inequalities with one variable by graphing on a number line. It explains the use of inequality symbols and demonstrates graphing techniques with open and closed circles. The tutorial includes examples of simple and complex inequalities, and applies these concepts to a real-world problem involving savings and earnings. By the end, viewers will understand how to represent and solve inequalities graphically.

What symbol would you use to show that a number is greater than another number?

• =

• ≤

• >

• <

How would you represent the inequality x < 10 on a number line?

• Open circle on 10 with arrow to the left

• Closed circle on 10 with arrow to the left

• Closed circle on 10 with arrow to the right

• Open circle on 10 with arrow to the right

What does a closed circle on a number line indicate?

• The number is not included in the solution set

• The inequality is an equation

• The inequality is invalid

• The number is included in the solution set

If you have the inequality x - 5 ≥ 6, what is the first step to solve it?

• Multiply both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

• Divide both sides by 5

After solving the inequality x - 5 ≥ 6, what is the solution for x?

• x ≥ 11

• x > 11

• x < 11

• x ≤ 11

In the context of inequalities, what does the arrow on a number line represent?

• The end of the solution set

• The direction of the inequality

• The midpoint of the solution set

• The start of the solution set

If you have $20 and earn $5 per hour, how many hours must you work to have at least $100?

• 15 hours

• 16 hours

• 20 hours

• 10 hours

What inequality represents the situation where you want at least $100 after earning $5 per hour starting with $20?

• 5l + 20 ≤ 100

• 5l + 20 = 100

• 5l + 20 ≥ 100

• 5l + 20 < 100

What does the variable 'l' represent in the inequality 5l + 20 ≥ 100?

• The number of lawns mowed

• The total money earned

• The number of hours worked

• The amount of money spent

If you mow more than 16 lawns, what will be the result?

• You will have less than $100

• You will have $80

• You will have exactly $100

• You will have more than $100