Interval Notation and Absolute Value

The video tutorial explains how to solve an absolute value inequality and express the solution in interval notation. It begins by isolating the absolute value, then applies a rule to solve the inequality. The tutorial includes a graphical representation using a number line and concludes with writing the solution in interval notation.

What is the first step in solving an absolute value inequality?

• Add a constant to both sides

• Combine like terms

• Isolate the absolute value expression

• Multiply both sides by a constant

How do you eliminate a constant from an absolute value inequality?

• Divide both sides by the constant

• Subtract the constant from both sides

• Multiply both sides by the constant

• Add the constant to both sides

What rule is used to handle absolute value inequalities?

• The division rule

• The absolute value rule

• The multiplication rule

• The addition rule

When applying the absolute value rule, what do you do with the inequality sign?

• Remove it

• Keep it the same

• Flip it and add a negative

• Change it to an equal sign

What is the next step after setting up the two inequalities?

• Clear fractions by multiplying

• Divide both sides by a constant

• Subtract a constant from both sides

• Add a constant to both sides

How do you solve the inequality x + 3 ≥ 12?

• x ≥ 15

• x ≤ 9

• x ≥ 9

• x ≤ 15

What does the number line represent in this context?

• The solution to the inequality

• The midpoint of the inequality

• The range of possible solutions

• The absolute value of the solution

What do brackets on a number line indicate?

• The solution is approximate

• The solution is exact

• The solution includes the endpoint

• The solution excludes the endpoint

How do you express the solution in interval notation?

• Using parentheses only

• Using absolute value symbols

• Using brackets only

• Using a combination of brackets and parentheses

What symbol is used to connect disjoint intervals in interval notation?

• Semicolon

• Comma

• Union symbol

• Colon