Understanding Absolute Value Inequalities

The video tutorial explains how to solve an absolute value inequality by isolating the absolute value, solving the resulting equations, and expressing the solution as a compound inequality. It demonstrates graphing the solution on a number line and using interval notation to represent the solution. Key steps include reversing the inequality symbol when dividing by a negative and understanding the concept of distance from zero in absolute value. The tutorial concludes with a comprehensive example, illustrating the union of intervals and the use of brackets and parentheses in interval notation.

What are the three forms in which we express the solution of an absolute value inequality?

• Equation, graph, and set notation

• Compound inequality, graph, and interval notation

• Inequality, table, and interval notation

• Equation, table, and set notation

What must you remember when dividing both sides of an inequality by a negative number?

• The inequality symbol remains the same

• The inequality symbol must be reversed

• The inequality symbol changes to an equal sign

• The inequality symbol becomes a greater than sign

What does the absolute value of a number represent?

• The number's distance from infinity

• The number itself

• The number's distance from zero

• The number's distance from one

How do you form a compound inequality from an absolute value equation?

• By creating two inequalities connected by 'and'

• By subtracting the absolute value from both sides

• By adding the absolute value to both sides

• By creating two inequalities connected by 'or'

What is the solution for the inequality |x - 5| = 1?

• x = 5 or x = 6

• x = 4 or x = 6

• x = 5 or x = 4

• x = 6 or x = 7

How do you represent the solution of an inequality on a number line?

• With dashed lines and arrows

• With open points and arrows

• With solid lines and arrows

• With closed points and arrows

What does the union of two intervals represent?

• The difference between the intervals

• The intersection of the intervals

• The product of the intervals

• The combination of the intervals

How is the interval from negative infinity to 4 represented in interval notation?

• [4, -∞)

• (-∞, 4)

• [4, ∞)

• (-∞, 4]

What symbol is used to denote the union of two intervals?

• ∩

• ∪

• ∧

• ∨

In interval notation, what type of bracket is used to indicate that an endpoint is included?

• Curly bracket

• Square bracket

• Angle bracket

• Round bracket