Solving Absolute Value Equations and Inequalities

The video tutorial covers absolute value equations and inequalities, explaining absolute value as a measure of distance from zero. It demonstrates solving equations and inequalities involving absolute values, providing methods and steps to find solutions. The tutorial also discusses the nature of solutions, including when there are two, one, or no solutions, and how to graph them. The video concludes with a final example emphasizing the importance of isolating the absolute value part of an equation.

What does the absolute value of a number represent?

• The number itself

• The distance from zero

• The negative of the number

• The square of the number

What is the absolute value of -3?

• -3

• 0

• 6

• 3

When solving the equation |2x - 1| = 5, what are the two possible equations you need to solve?

• 2x + 1 = 5 and 2x - 1 = 0

• 2x - 1 = 5 and 2x + 1 = 5

• 2x - 1 = 5 and 2x - 1 = -5

• 2x + 1 = 5 and 2x + 1 = -5

What are the solutions for the equation |2x - 1| = 5?

• x = -2 and x = 3

• x = 0 and x = 5

• x = 2 and x = -3

• x = 1 and x = -1

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

• Multiply both sides by a constant

• Isolate the absolute value part of the equation

• Add a constant to both sides

• Subtract a constant from both sides

How many solutions does an absolute value equation have if it equals a positive number?

• One

• Infinite

• Two

• None

What does it mean if an absolute value equation equals a negative number?

• It has infinite solutions

• It has two solutions

• It has one solution

• It has no solution

How do you set up an inequality for |2x - 1| ≥ 5?

• 2x - 1 ≤ 5 and 2x - 1 ≤ -5

• 2x - 1 ≤ 5 and 2x - 1 ≥ -5

• 2x - 1 ≥ 5 and 2x - 1 ≥ -5

• 2x - 1 ≥ 5 and 2x - 1 ≤ -5

When graphing the solution for |2x - 1| ≥ 5, what type of circles do you use at the boundary points?

• No circles

• Open circles

• Closed circles

• Half-filled circles

What is the first step in solving the inequality 3|x - 1| = 6?

• Add 3 to both sides

• Subtract 3 from both sides

• Divide both sides by 3

• Multiply both sides by 3