Solving Absolute Value Inequalities Challenge

This video tutorial covers solving absolute value inequalities. It begins with an introduction to absolute value and its properties, explaining how it represents a number's distance from zero on a number line. The tutorial then delves into solving absolute value inequalities, distinguishing between 'or' and 'and' statements. Through examples, it demonstrates how to convert absolute value inequalities into compound inequalities and solve them. The video concludes with a practice problem to reinforce the concepts learned.

What do the two bars around a quantity represent in an absolute value inequality?

• Inequality symbols

• Absolute value symbols

• Parentheses

• Brackets

What is the absolute value of -3?

• -3

• 0

• 6

• 3

What type of statement is formed when the absolute value of a quantity is greater than or equal to a number?

• A 'nor' statement

• An 'and' statement

• An 'or' statement

• A 'but' statement

In the inequality |X - 3| ≥ 7, what is the first step to solve it?

• Multiply both sides by 7

• Add 3 to both sides

• Write two inequalities

• Subtract 3 from both sides

When solving the inequality |2X - 3| > 1, what must you do to the inequality sign in the second inequality?

• Keep it the same

• Flip it and make the number negative

• Flip it and make the number positive

• Remove it

What does the solution set for the inequality |X - 3| ≥ 7 look like on a number line?

• Numbers greater than or equal to -10 and less than or equal to 4

• Numbers between -4 and 10

• Numbers less than or equal to -4 or greater than or equal to 10

• Numbers between -10 and 4

What type of statement is formed when the absolute value of a quantity is less than or equal to a number?

• A 'but' statement

• An 'and' statement

• A 'nor' statement

• An 'or' statement

In the inequality |X - 9| ≤ 3, what is the first step to solve it?

• Subtract 9 from both sides

• Multiply both sides by 3

• Write one large compound inequality

• Add 9 to both sides

What does the solution set for the inequality |X - 9| ≤ 3 look like on a number line?

• Numbers between 6 and 12

• Numbers between -3 and 9

• Numbers greater than or equal to -9 and less than or equal to 3

• Numbers less than or equal to 6 or greater than or equal to 12

What should you do if you encounter an absolute value inequality with numbers outside the absolute value bars?

• Multiply the numbers outside by the absolute value

• Solve the numbers outside first

• Combine the numbers with the absolute value

• Ignore the numbers outside