Solving Absolute Value Inequalities

This video tutorial covers advanced techniques for solving absolute value inequalities. It begins with a refresher on basic absolute value inequalities and progresses to more complex examples, including rational inequalities. The tutorial provides step-by-step solutions and graphical representations to enhance understanding.

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

• Isolate the absolute value expression.

• Add a constant to both sides.

• Multiply both sides by a negative number.

• Square both sides.

If |X| > a, where a is a positive number, what can be concluded?

• X is between -a and a.

• X is greater than a or less than -a.

• X is less than a.

• X is equal to a.

What does the inequality |X| < a imply?

• X is equal to a.

• X is between -a and a.

• X is less than -a.

• X is greater than a.

What is the solution to |X| < 0?

• All real numbers.

• No solution.

• X is greater than 0.

• X is less than 0.

What is the solution to |X| > a, where a is a negative number?

• All real numbers.

• No solution.

• X is greater than a.

• X is less than a.

In the inequality |X + 3| > |2X - 1|, what is the first step?

• Set X + 3 equal to 2X - 1.

• Find where each expression inside the absolute value is zero.

• Add 3 to both sides.

• Multiply both sides by 2.

How do you handle the inequality |X + 5| + |X - 3| > 14?

• Subtract 14 from both sides.

• Set each expression inside the absolute value to zero.

• Combine the absolute values into one expression.

• Multiply both sides by 14.

What is the approach to solve |3/(X - 1)| > 5?

• Multiply both sides by X - 1.

• Add 5 to both sides.

• Consider the cases where 3/(X - 1) is greater than 5 and less than -5.

• Set 3/(X - 1) equal to 5.