Understanding Absolute Value Equations

The video tutorial explains how to solve an absolute value equation, specifically 3x - 9 = 0, and graph the solution on a number line. It begins by discussing the properties of absolute values, emphasizing that the absolute value of a number is its distance from zero. The tutorial then walks through solving the equation by isolating the variable x, resulting in x = 3. Finally, it verifies the solution by substituting it back into the original equation to ensure it satisfies the condition.

What is the first step in solving the equation |3x - 9| = 0?

• Multiply both sides by 3

• Subtract 9 from both sides

• Add 9 to both sides

• Divide both sides by 3

When the absolute value of an expression equals zero, what can we infer about the expression?

• The expression is zero

• The expression is undefined

• The expression is negative

• The expression is positive

What is the absolute value of 0?

• 1

• 0

• -1

• Undefined

What does the absolute value of a number represent?

• Its distance from 10 on the number line

• Its distance from -1 on the number line

• Its distance from 1 on the number line

• Its distance from 0 on the number line

What is the unique property of the number 0 in terms of absolute value?

• It is the only number with an absolute value of 1

• It is the only number with an absolute value of 0

• It has no absolute value

• It has multiple absolute values

What operation is performed after adding 9 to both sides of the equation 3x - 9 = 0?

• Subtract 9 from both sides

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

What is the value of x that satisfies the equation 3x - 9 = 0?

• x = 0

• x = 1

• x = 2

• x = 3

What is the result of dividing 9 by 3 in the equation 3x = 9?

• 1

• 2

• 3

• 4

How do you verify the solution x = 3 for the equation |3x - 9| = 0?

• Substitute x = 3 into the equation and check if it equals 1

• Substitute x = 3 into the equation and check if it equals 0

• Substitute x = 3 into the equation and check if it equals -1

• Substitute x = 3 into the equation and check if it equals 9

What is the final step in verifying the solution to the equation |3x - 9| = 0?

• Check if the absolute value equals -1

• Check if the absolute value equals 9

• Check if the absolute value equals 0

• Check if the absolute value equals 1