Understanding Absolute Value Inequalities

The video tutorial explains how to solve absolute value inequalities by first understanding the concept of absolute value as the distance from zero on a number line. It then guides viewers through isolating the absolute value in an equation, setting up two cases (positive and negative), and solving these equations. Finally, it emphasizes the importance of checking solutions to ensure accuracy.

What is the absolute value of -4?

• 0

• 8

• -4

• 4

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

• Add a constant to both sides

• Square both sides

• Isolate the absolute value

• Multiply by a negative number

When isolating the absolute value, what operation is used if the absolute value is multiplied by -5?

• Divide by -5

• Subtract 5

• Multiply by 5

• Add 5

Why do we set up two cases when solving absolute value equations?

• To account for both positive and negative scenarios

• To find the maximum value

• To simplify the equation

• To eliminate fractions

What are the two cases set up for the equation |6a + 2| = 3?

• 6a + 2 = 3 and 6a + 2 = -3

• 6a + 2 = 3 and 6a - 2 = 3

• 6a + 2 = 0 and 6a + 2 = 6

• 6a + 2 = 3 and 6a + 2 = 0

What is the solution for the equation 6a + 2 = 3?

• a = 1/2

• a = 1/3

• a = 1/6

• a = 1

What is the solution for the equation 6a + 2 = -3?

• a = -1/6

• a = -5/6

• a = -1/3

• a = -1/2

Why is it important to check solutions in absolute value equations?

• To simplify the equation

• To find additional solutions

• To eliminate negative values

• To verify the solutions are correct

What is the absolute value of 6 * 1 + 2?

• 6

• 8

• 3

• 1

What is the final step in solving absolute value inequalities?

• Multiply by a constant

• Check your work

• Divide by a constant

• Add a constant