Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations. It begins by outlining the general steps: isolating the absolute value, setting up two equations, and checking solutions. The first example demonstrates solving an equation where the absolute value equals a positive number, resulting in two solutions. The second example shows a case where the absolute value equals a negative number, leading to no solution. The tutorial emphasizes understanding the concept of absolute value as a number's distance from zero and highlights that it cannot be negative.

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

• Isolate the absolute value

• Multiply both sides by 2

• Check the solution

• Set up two equations

Why do we set up two equations when solving an absolute value equation?

• To find the average

• To eliminate fractions

• To account for both positive and negative solutions

• To simplify the equation

What is the solution to the equation 2x - 3 = 12?

• x = 3

• x = 15/2

• x = 9

• x = 6

What is the solution to the equation 2x - 3 = -12?

• x = 9/2

• x = 0

• x = -6

• x = -9/2

What does the absolute value of a number represent?

• The number's distance from ten

• The number's distance from one

• The number's distance from zero

• The number's distance from negative one

What is the absolute value of -12?

• 0

• 24

• -12

• 12

What is the result of solving the equation 2x = 15?

• x = 15

• x = 30

• x = 7.5

• x = 0

What is the absolute value of 12?

• 24

• -12

• 12

• 0

Why does the equation |1 - 3x| = -2 have no solution?

• Because the equation is not simplified

• Because x is not a real number

• Because absolute values cannot be negative

• Because 1 - 3x is always positive

What should you conclude if an absolute value equation equals a negative number?

• The equation is undefined

• The equation has two solutions

• The equation has one solution

• The equation has no solution