Understanding Inequalities and Graphing

This video tutorial explains how to graph inequalities using closed and open circles. It covers when to use a closed circle, which is used for 'greater than or equal to' or 'less than or equal to' inequalities, and provides examples with y ≤ 5 and -3 ≤ w. The tutorial also explains how to determine which side of the number line to shade, emphasizing the importance of understanding the direction of inequalities.

What is the primary focus of this video tutorial?

• Graphing inequalities

• Solving equations

• Calculating derivatives

• Finding integrals

When graphing inequalities, when should you use a closed circle?

• When the inequality is not equal to

• When the inequality is greater than

• When the inequality is less than

• When the inequality includes 'or equal to'

What does a closed circle on a number line represent?

• The number is not part of the solution set

• The number is a variable

• The number is part of the solution set

• The number is an approximation

In the inequality y ≤ 5, which side of the number line should be shaded?

• Neither side of 5

• Both sides of 5

• The left side of 5

• The right side of 5

How can the inequality y ≤ 5 be alternatively expressed?

• 5 < y

• y = 5

• 5 ≥ y

• y > 5

What numbers are to the left of 5 on a number line?

• 6, 7, 8

• 5, 6, 7

• 4, 3, 2

• 10, 11, 12

Which of the following is NOT a number to the left of 5?

• 2

• 3

• 4

• 6

In the inequality -3 ≤ w, where should the closed circle be placed?

• On -4

• On -3

• On -2

• On 0

Which side of the number line is shaded for the inequality -3 ≤ w?

• The right side of -3

• Both sides of -3

• The left side of -3

• Neither side of -3

How can the inequality -3 ≤ w be alternatively expressed?

• w > -3

• w < -3

• w ≥ -3

• w = -3