Solving Equations and Inequalities with Absolute Value

This video tutorial covers section 3.5 on solving equations and inequalities involving absolute values. It begins with a refresher on absolute value concepts, highlighting common student mistakes. The tutorial then explains strategies for solving absolute value equations and inequalities, including isolating the absolute value and splitting equations into positive and negative parts. It also covers compound inequalities, graphing solutions, and advanced techniques for solving inequalities. The video concludes with a practical exercise for students to apply their learning.

What is the absolute value of -5?

• 5

• 10

• 0

• -5

Which of the following is a common mistake when dealing with absolute values?

• Absolute value of a negative number is its positive counterpart

• Absolute value of x plus 3 is equal to absolute value of x plus absolute value of 3

• Absolute value of a positive number is the number itself

• Absolute value of x is always positive

What should you do first when solving an absolute value equation?

• Multiply both sides by a constant

• Subtract a constant from both sides

• Isolate the absolute value expression

• Add a constant to both sides

If |x - 3| = 5, what are the possible values of x?

• x = 8 or x = -2

• x = 5 or x = -5

• x = 3 or x = -3

• x = 2 or x = -8

When solving |x - 3| = 5, what are the two equations you need to solve?

• x + 3 = 5 and x + 3 = -5

• x + 3 = 5 and x - 3 = 5

• x - 3 = 5 and x - 3 = -5

• x - 3 = 5 and x + 3 = 5

How do you translate the inequality |x| < a?

• -a < x < a

• |x| > a

• x < a

• x > -a

What is the correct way to handle the inequality |x| > a?

• x > a or x < -a

• x > -a

• |x| < a

• x < a

If |3x + 2| < 5, what is the range of x?

• -5 < x < 5

• -2 < x < 2

• -1 < x < 7/3

• -7/3 < x < 1

What must you remember when dividing both sides of an inequality by a negative number?

• Subtract a constant from both sides

• Add a constant to both sides

• Keep the inequality sign the same

• Flip the inequality sign

In the inequality |x - 3| ≥ 1, what are the two inequalities you need to solve?

• x - 3 ≤ 1 and x - 3 ≥ -1

• x + 3 ≤ 1 and x + 3 ≥ -1

• x + 3 ≥ 1 and x + 3 ≤ -1

• x - 3 ≥ 1 and x - 3 ≤ -1