Understanding Absolute Value Inequalities

This video tutorial explains how to solve two types of absolute value inequalities. The first example involves solving the inequality 2x + 3 < 7 by expressing it as a compound inequality, graphing it, and using interval notation. The second example addresses the inequality 3x - 1 = 5, demonstrating how to solve it and graph the solution as a union of intervals. The video provides step-by-step instructions for solving, graphing, and interpreting these inequalities using interval notation.

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

• Express it as a compound inequality

• Use logarithmic functions

• Convert it to a quadratic equation

• Graph it directly on a number line

When solving the inequality |2x + 3| < 7, what are the two inequalities formed?

• 2x + 3 > 7 and 2x + 3 < -7

• 2x + 3 < 7 and 2x + 3 > -7

• 2x + 3 < 0 and 2x + 3 > 0

• 2x + 3 < 7 and 2x + 3 > 7

What does the intersection of the intervals x < 2 and x > -5 represent?

• The union of the intervals

• The solution to the inequality

• The absolute value of the intervals

• The midpoint of the intervals

In the second example, what does the inequality |3x - 1| = 5 represent?

• A quadratic equation

• A single inequality

• A linear equation

• Two inequalities connected by 'or'

What are the two inequalities formed from |3x - 1| = 5?

• 3x - 1 = 0 and 3x - 1 = 5

• 3x - 1 > 5 and 3x - 1 < -5

• 3x - 1 < 5 and 3x - 1 > -5

• 3x - 1 = 5 and 3x - 1 = -5

What is the solution for the inequality 3x - 1 = 5?

• x = 2

• x = 4

• x = 1

• x = 3

How is the interval from -4/3 to negative infinity represented in interval notation?

• [-4/3, ∞)

• (-∞, -4/3]

• (-4/3, ∞)

• (-∞, -4/3)

What does the union of intervals represent in the context of absolute value inequalities?

• The intersection of the intervals

• The combined solution of the inequalities

• The midpoint of the intervals

• The absolute value of the intervals

What is the graphical representation of x = 2 in the second example?

• A closed point at 2 with an arrow to the right

• An open point at 2 with an arrow to the left

• An open point at 2 with an arrow to the right

• A closed point at 2 with an arrow to the left

What is the significance of using a square bracket in interval notation?

• It indicates the interval is open

• It denotes the absolute value of the interval

• It represents the midpoint of the interval

• It shows the interval is closed