Inequalities and Graphing Concepts

This video tutorial covers graphing linear inequalities in one variable, focusing on using number lines. It explains how to determine solution sets using set notation and graph these solutions. The tutorial also covers advanced graphing techniques and how to write inequalities from given graphs. The lesson includes practical examples and exercises to reinforce understanding.

Which of the following symbols represents 'less than or equal to'?

• <=

• >

• !=

• <

If 3x + 4 < 19, which of the following values for x is a solution?

• 0

• 11

• 19

• 5

How many solutions are there typically for an inequality?

• One

• Two

• A finite number

• An infinite number

When graphing the inequality U > -2, what should be done at -2 on the number line?

• Place a filled circle

• Place an empty circle

• Shade the circle

• Do nothing

For the inequality T ≥ 2.5, how should the number line be marked at 2.5?

• With an empty circle

• With a filled circle

• With no circle

• With a shaded circle

If a graph shows a filled circle at 3 and 1/3 and shading to the left, what is the inequality?

• y ≥ 3 and 1/3

• y > 3 and 1/3

• y ≤ 3 and 1/3

• y < 3 and 1/3

What inequality represents a graph with an empty circle at 0.5 and shading to the right?

• x ≤ 0.5

• x ≥ 0.5

• x < 0.5

• x > 0.5

If a graph has a filled circle at 12 and shading to the right, what is the inequality?

• x < 12

• x ≤ 12

• x > 12

• x ≥ 12

What is the inequality for a graph with a filled circle at 2 and shading to the left?

• x > 2

• x < 2

• x ≥ 2

• x ≤ 2

What inequality represents the temperatures at which water is a gas, given that it boils at 100°C?

• T ≥ 100°C

• T > 100°C

• T ≤ 100°C

• T < 100°C