Inequalities and Their Representations

In this video, Mr. J explains how to solve and graph compound inequalities involving 'and'. He uses an example problem, 4C - 5 ≥ -9 and < 7, to demonstrate the process. The video covers isolating the variable, using inverse operations, and graphing the solution on a number line. The solution is shown to be C ≥ -1 and < 3, and Mr. J illustrates how to represent this on a number line with filled and open circles. The video concludes with a recap of the steps involved in solving and graphing compound inequalities.

What is the first step in solving a compound inequality involving 'and'?

• Add the same number to all parts of the inequality

• Isolate the variable

• Multiply all parts of the inequality by the same number

• Graph the solution on a number line

When isolating the variable, what operation should be undone first in the inequality 4C - 5?

• Subtraction

• Division

• Multiplication

• Addition

What is the inverse operation of subtraction?

• Addition

• Division

• Multiplication

• Subtraction

After adding 5 to all parts of the inequality, what is the resulting inequality?

• 4C <= -4 and > 12

• 4C >= -4 and > 12

• 4C > -4 and < 12

• 4C >= -4 and < 12

What operation is used to isolate C after obtaining 4C >= -4 and < 12?

• Division

• Subtraction

• Addition

• Multiplication

What is the final solution for C after solving the inequality?

• C > -1 and < 3

• C >= -1 and <= 3

• C >= -1 and < 3

• C > -1 and <= 3

On a number line, how is the point -1 represented for the inequality C >= -1?

• Arrow

• Closed circle

• Open circle

• Dashed line

How is the point 3 represented on the number line for the inequality C < 3?

• Dashed line

• Open circle

• Arrow

• Closed circle

What does the shaded region between -1 and 3 on the number line represent?

• Values of C that satisfy only one inequality

• Values of C that satisfy both inequalities

• Values of C that are greater than 3

• Values of C that are less than -1

What is the main takeaway from solving and graphing compound inequalities?

• The solution is always a single point

• Graphing is not necessary

• Both inequalities must be satisfied simultaneously

• Only one inequality needs to be satisfied