Solving Absolute Value Inequalities and Graphing Solutions

This video tutorial covers solving two types of absolute value inequalities. The first example demonstrates solving the inequality 2X + 3 < 7 by expressing it as a compound inequality, graphing it, and using interval notation. The second example involves solving the inequality 3X - 1 = 5, focusing on finding the union of two 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?

• Using interval notation

• Graphing the inequality

• Writing it as a compound inequality

• Finding the intersection of intervals

In the inequality |2x + 3| < 7, what does the first inequality become?

• 2x + 3 < -7

• 2x + 3 < 7

• 2x + 3 > 7

• 2x + 3 > -7

What is the second inequality derived from |2x + 3| < 7?

• 2x + 3 < 7

• 2x + 3 > 7

• 2x + 3 < -7

• 2x + 3 > -7

What is the solution to the inequality 2x + 3 < 7 after solving for x?

• x < 2

• x > -2

• x > 2

• x < -2

What is the interval notation for the solution of |2x + 3| < 7?

• [5, -2)

• (-5, 2]

• [-5, 2]

• (-5, 2)

In the inequality |3x - 1| > 5, what does the first inequality become?

• 3x - 1 > 5

• 3x - 1 > -5

• 3x - 1 < -5

• 3x - 1 < 5

What is the second inequality derived from |3x - 1| > 5?

• 3x - 1 < 5

• 3x - 1 > 5

• 3x - 1 > -5

• 3x - 1 < -5

What is the solution to the inequality 3x - 1 > 5 after solving for x?

• x > -2

• x < 2

• x > 2

• x < -2

What is the interval notation for the solution of |3x - 1| > 5?

• (-∞, -4/3] U [2, ∞)

• (-∞, -4/3] U (2, ∞)

• (-∞, -4/3) U [2, ∞)

• (-∞, -4/3) U (2, ∞)

What does the 'U' symbol represent in interval notation?

• Intersection

• Union

• Inequality

• Absolute value