Mastering Absolute Value Equations and Inequalities

The video tutorial covers solving absolute value equations and inequalities using a unified method. It begins with a definition of absolute value as the distance from zero on a number line, emphasizing that it is always positive. The tutorial explains how to solve equations by considering both the 'as is' and 'opposite' scenarios. It also covers solving inequalities, highlighting the importance of switching inequality signs when multiplying or dividing by a negative number. The video includes practice problems with solutions and encourages students to seek help if needed.

What is the absolute value of -3?

• 3

• 6

• 0

• -3

Which of the following statements is true about absolute values?

• Absolute value is the same as the original number.

• Absolute value is always zero.

• Absolute value represents the distance from zero.

• Absolute value can be negative.

If the absolute value of x is 5, what are the possible values of x?

• 5 and -5

• 5 and 0

• 0 and -5

• 5 and 10

When solving the equation |x + 2| = 7, what are the two possible equations you need to solve?

• x + 2 = 7 and x + 2 = -7

• x + 2 = 7 and x + 2 = 0

• x + 2 = 7 and x - 2 = 7

• x - 2 = 7 and x - 2 = -7

What is the first step in solving the equation |3x + 1| = 10?

• Multiply both sides by 3

• Subtract 1 from both sides

• Add 1 to both sides

• Divide both sides by 3

In the equation |2x - 3| = 5, what are the two possible values of x?

• 4 and 0

• 4 and -1

• 4 and 1

• 4 and -4

When solving the inequality |x - 4| < 3, what are the two resulting inequalities?

• x - 4 > 3 and x - 4 > -3

• x - 4 < 3 and x - 4 < -3

• x - 4 < 3 and x - 4 > 3

• x - 4 < 3 and x - 4 > -3

What must you remember to do when you multiply or divide both sides of an inequality by a negative number?

• Add 1 to both sides

• Subtract 1 from both sides

• Keep the inequality sign the same

• Switch the inequality sign

In the inequality |x + 2| ≥ 5, what are the two resulting inequalities?

• x + 2 ≤ 5 and x + 2 ≤ -5

• x + 2 ≥ 5 and x + 2 ≥ -5

• x + 2 ≥ 5 and x + 2 ≤ -5

• x + 2 ≤ 5 and x + 2 ≥ -5

What is the interval notation for the solution to the inequality |x - 1| < 4?

• (-3, 5)

• (-4, 4)

• (-3, 3)

• (-5, 5)