Solving Absolute Value Equations

The video tutorial explains how to solve absolute value equations by isolating the absolute value and setting up two equations. It provides two examples: one where the equation has two solutions and another where the equation has no solution due to a negative absolute value. The tutorial emphasizes checking solutions and understanding the concept of absolute value as a distance from zero.

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

• Check the solution

• Multiply both sides by 2

• Isolate the absolute value

• Set up two equations

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

• To find the average

• To account for both positive and negative solutions

• To simplify the equation

• To eliminate fractions

In the first example, what are the two possible equations derived from the absolute value equation?

• 2x - 3 = 0 and 2x - 3 = 12

• 2x + 3 = 0 and 2x + 3 = 12

• 2x - 3 = 12 and 2x - 3 = -12

• 2x + 3 = 12 and 2x + 3 = -12

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

• x = 6

• x = 3

• x = 9

• x = 15/2

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

• x = -6

• x = -9/2

• x = 9/2

• x = 0

Why does the second example have no solution?

• The equation is too complex

• Absolute value cannot equal a negative number

• The variable is missing

• The equation is not isolated

What is the absolute value of a number?

• The number divided by two

• The number's distance from zero

• The number squared

• The number itself

What happens if an absolute value equation equals a negative number?

• It has one solution

• It has infinite solutions

• It has two solutions

• It has no solution

What should you do if you mistakenly set up equations for an absolute value equal to a negative number?

• Multiply by -1

• Check the original equation

• Ignore the negative sign

• Solve them anyway

What is the key takeaway from the second example?

• No solution if absolute value equals a negative

• Absolute values can be negative

• Equations must be simplified

• Always solve for x