Understanding Absolute Value Equations

In this video, Mr. J explains how to solve absolute value equations, focusing on equations with numbers and operations outside the absolute value. He provides three examples, demonstrating the process of isolating the absolute value, writing two equations, and solving for the variable. Each example is followed by a verification step to ensure the solutions are correct. The video emphasizes the importance of understanding the inverse operations and the concept of absolute value.

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

• Use the distributive property

• Multiply both sides by a constant

• Isolate the absolute value

• Add a constant to both sides

In the first example, what operation is used to isolate the absolute value?

• Subtraction

• Division

• Multiplication

• Addition

What are the two possible values for x in the equation |x - 6| = 2?

• x = 8 and x = -8

• x = 6 and x = -6

• x = 4 and x = -4

• x = 2 and x = -2

Why can't the distributive property be used with absolute values?

• Absolute values are not numbers

• Absolute values are not the same as parentheses

• Absolute values are always positive

• Absolute values are variables

What is the inverse operation of multiplication used in the second example?

• Subtraction

• Addition

• Exponentiation

• Division

In the second example, what are the two solutions for G?

• G = 5 and G = -5

• G = 7 and G = -7

• G = 3 and G = -17

• G = 10 and G = -10

In the third example, what is the first operation used to isolate the absolute value?

• Subtraction

• Addition

• Multiplication

• Division

What is the result of dividing both sides by 5 in the third example?

• The absolute value is isolated

• The equation is simplified

• The variable is isolated

• The equation is solved

What is the final step in solving the equation 5 * |3x - 15| + 4 = 49?

• Subtract 4 from both sides

• Divide both sides by 5

• Add 4 to both sides

• Multiply both sides by 5

What is the purpose of checking solutions by plugging them back into the original equation?

• To find new solutions

• To verify the solutions are correct

• To isolate the variable

• To simplify the equation