Understanding Inequalities and Their Graphs

In this video, Mr. J explains how to solve and graph one-step division inequalities. He emphasizes the importance of isolating the variable using inverse operations and highlights the need to flip the inequality symbol when multiplying or dividing by a negative number. The video includes two examples: solving x/4 ≤ 12 and W/-9 < 7, with detailed steps and graphing instructions. Mr. J also checks solutions to ensure accuracy and concludes with a brief summary.

What is the primary goal when solving inequalities?

• To find the exact value of the variable

• To isolate the variable on one side

• To eliminate all variables

• To make both sides equal

When solving x/4 ≤ 12, what operation is used to isolate x?

• Division

• Multiplication

• Subtraction

• Addition

What does a filled circle on a number line represent in graphing inequalities?

• The inequality is reversed

• The inequality is incorrect

• The number is included

• The number is not included

Which value can be used to verify the solution of x/4 ≤ 12?

• 70

• 50

• 40

• 60

What happens to the inequality symbol when both sides are multiplied by a negative number?

• It remains the same

• It flips direction

• It becomes an equal sign

• It disappears

What is the solution to the inequality W/-9 < 7?

• W ≤ -63

• W > -63

• W = -63

• W < -63

In the inequality W > -63, what does an open circle on the number line indicate?

• The number is not included

• The number is included

• The inequality is incorrect

• The inequality is reversed

Which value can be used to verify the solution of W > -63?

• -63

• -80

• -54

• -70

What is the result of -54 divided by -9?

• 8

• 7

• 6

• 5

What does the arrow direction on a number line indicate in graphing inequalities?

• The direction of increasing numbers

• The direction of decreasing numbers

• The direction of the variable

• The direction of the inequality solutions