Graphing and Solving Inequalities

This video tutorial covers compound inequalities, explaining how they combine two sets of inequalities using 'and' or 'or' statements. It details the graphical representation of these statements, how to write them in a single expression, and methods for solving them. Special cases are also discussed, providing a comprehensive understanding of compound inequalities.

What is a compound inequality?

• A combination of two inequalities

• An equation with no solution

• A single inequality with two variables

• An equation with one variable

In an 'and' statement, what does the graph represent?

• The union of two graphs

• The intersection of two graphs

• The difference between two graphs

• The sum of two graphs

What is the graphical representation of X < 4 and X ≥ 2?

• A line from 2 to 4 with closed circles at both ends

• A line from 2 to 4 with a closed circle at 2

• A line from 2 to 4 with an open circle at 4

• A line from 2 to 4 with open circles

In an 'or' statement, what does the graph represent?

• The union of two graphs

• The intersection of two graphs

• The sum of two graphs

• The difference between two graphs

How is X < 7 or X ≥ 9 represented on a graph?

• Two separate lines, one starting at 7 and another at 9

• A line from 7 to 9 with a closed circle at 9

• A single line from 7 to 9

• A line from 7 to 9 with open circles

How can you write a compound inequality in one expression?

• Only for 'and' statements

• Only for 'or' statements

• For both 'and' and 'or' statements

• It is not possible

What is the correct way to write X > -8 and X ≤ 4?

• -8 < X ≤ 4

• X < -8 and X ≥ 4

• X > -8 or X ≤ 4

• -8 > X < 4

When solving 'and' inequalities, what must you do to each part?

• Multiply each part by the same number

• Subtract the same number from each part

• Divide each part by the same number

• Add the same number to each part

What is the solution to the inequality -2 < X < 5?

• X is greater than 5

• X is between -2 and 5, exclusive

• X is between -2 and 5, inclusive

• X is any number

How do you solve 'or' inequalities?

• Ignore one of the inequalities

• Solve each inequality separately

• Combine the inequalities into one

• Solve only the first inequality