Solving Absolute Value Inequalities Explained

This video tutorial covers solving compound inequalities, focusing on absolute value inequalities. It introduces the concepts of 'more is or' and 'less is nest' to help understand when to use 'or' and 'nest' in inequalities. The tutorial provides step-by-step examples of solving and graphing these inequalities on number lines and coordinate planes. It also includes practice problems for viewers to solve and graph, reinforcing the concepts taught.

What is the mnemonic used to remember the rules for solving compound inequalities?

• Greater is better, lesser is worse

• Greater is or, lesser is nest

• More is or, less is nest

• More is less, less is more

How do you graph the inequality n > 5 or n < -5 on a number line?

• A dashed line between 5 and -5

• Two open points at 5 and -5 with arrows pointing outward

• Two closed points at 5 and -5 with arrows pointing inward

• A filled line segment between 5 and -5

What does the inequality |n| > 5 translate to?

• n < 5 and n > -5

• n > 5 and n < -5

• n < 5 or n > -5

• n > 5 or n < -5

What does 'less is nest' mean in the context of inequalities?

• The expression has no boundary points

• The expression is less than a certain value

• The expression is greater than a certain value

• The expression is nested between two boundary points

How do you solve the inequality |3x - 12| ≥ 6?

• 3x - 12 > 6 and 3x - 12 < -6

• 3x - 12 < 6 and 3x - 12 > -6

• 3x - 12 ≤ 6 or 3x - 12 ≥ -6

• 3x - 12 ≥ 6 or 3x - 12 ≤ -6

How do you graph the inequality 3x + 4 < 10 on a coordinate plane?

• Use solid lines for boundary lines and shade in between

• Use dashed lines for boundary lines and shade in between

• Use dashed lines for boundary lines and shade outside

• Use solid lines for boundary lines and shade outside

What is the solution to the inequality |3x + 4| < 10?

• 3x + 4 < 10 or 3x + 4 > -10

• -10 < 3x + 4 < 10

• -10 > 3x + 4 > 10

• 3x + 4 > 10 and 3x + 4 < -10

What is the first step in solving the inequality |6r - 3| ≤ 21?

• Divide each side by 6

• Multiply each side by 6

• Subtract 3 from each side

• Add 3 to each side

What is the final step in solving the inequality |6r - 3| ≤ 21?

• Multiply each side by 6

• Subtract 3 from each side

• Add 3 to each side

• Divide each side by 6

How do you graph the inequality |b - 4| > 6 on a number line?

• A filled line segment between 10 and -2

• Two closed points at 10 and -2 with arrows pointing inward

• Two open points at 10 and -2 with arrows pointing outward

• A dashed line between 10 and -2