Solving Absolute Value Equations and Inequalities

The video tutorial covers solving absolute value equations and inequalities, using a jail analogy to explain the concept. It demonstrates solving equations by considering both positive and negative solutions, and highlights scenarios where no solution exists. The tutorial also addresses extraneous solutions, emphasizing the importance of checking solutions. Practice problems are provided to reinforce learning.

What does the absolute value of a number represent?

• The number itself

• The distance from zero

• The negative of the number

• The square of the number

If the absolute value of -4 is 4, what is the absolute value of 4?

• 0

• 4

• 8

• -4

When solving an absolute value equation, how many equations do you typically write?

• Four

• One

• Two

• Three

In the equation |2x - 9| = 15, what are the two possible equations you need to solve?

• 2x - 9 = 15 and 2x - 9 = -15

• 2x - 9 = 15 and 2x + 9 = 15

• 2x + 9 = 15 and 2x - 9 = 0

• 2x - 9 = 0 and 2x + 9 = 15

What does it mean if an absolute value equation equals a negative number?

• The solution is zero

• There are two solutions

• There is one solution

• There is no solution

In the equation |1/2x + 3| = 2, what is the first step to isolate the absolute value?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 3 from both sides

• Add 3 to both sides

What is an extraneous solution?

• A solution that does not satisfy the original equation

• A solution that is always negative

• A solution that is always positive

• A solution that works for all equations

Why is it important to check solutions in absolute value equations?

• To find the positive solution

• To find the negative solution

• To identify extraneous solutions

• To simplify the equation

In the equation |5x - 6| = x, what are the two possible equations to solve?

• 5x + 6 = x and 5x - 6 = 0

• 5x - 6 = 0 and 5x + 6 = x

• 5x - 6 = x and 5x + 6 = x

• 5x - 6 = x and 5x - 6 = -x

What should you do if you find an extraneous solution?

• Include it in the final answer

• Ignore it

• Double-check the calculations

• Use it to find another solution