Solving Absolute Value Equations and Inequalities

The video tutorial covers the basics of absolute value, explaining it as the distance from zero, and demonstrates how to solve absolute value equations and inequalities. It discusses the concept of having two solutions for equations and the importance of setting up two cases. The tutorial also explains how to handle complex equations and inequalities, emphasizing the need to isolate the absolute value and consider both positive and negative scenarios. The video concludes with examples of solving inequalities using number lines and compound inequalities.

What does the absolute value of a number represent?

• The distance from zero

• The number itself

• The square of the number

• The negative of the number

If the absolute value of x equals 3, what are the possible values of x?

• 3 and 0

• 3 and 6

• 3 and -3

• 0 and -3

What is the solution to the equation |x + 7| = 10?

• x = 10 and x = -10

• x = 3 and x = -17

• x = 17 and x = -3

• x = 7 and x = -7

In the equation |4x - 5| = 14, what should be done first?

• Subtract 5

• Add 5

• Multiply by 4

• Divide by 4

What are the solutions to the equation |4x - 5| = 14?

• x = 5 and x = -5

• x = 4 and x = -4

• x = 2 and x = -2

• x = 7 and x = 3

Why does the equation |x| = -3 have no solution?

• Because x cannot be negative

• Because absolute value cannot be negative

• Because x must be positive

• Because x must be zero

Which of the following is a solution to the inequality |x| > 3?

• x = 2

• x = -2

• x = 4

• x = 0

Which of the following is NOT a solution to the inequality |x| < 3?

• x = -2

• x = 4

• x = 0

• x = 2

In the inequality |x| > 3, which range of values for x is correct?

• x > 3 or x < -3

• x > 3 and x < -3

• x > -3 and x < 3

• x > 0 and x < 3

How should the inequality |7x + 14| ≥ 70 be written in two cases?

• 7x + 14 < 70 and 7x + 14 > -70

• 7x + 14 > 70 and 7x + 14 < -70

• 7x + 14 ≤ 70 and 7x + 14 ≥ -70

• 7x + 14 ≥ 70 and 7x + 14 ≤ -70