Understanding Absolute Value Equations

This video tutorial by Mr. J covers absolute value equations, explaining how to solve them when they have two solutions, one solution, or no solution. The video provides examples for each case, demonstrating the process of isolating the absolute value and solving the resulting equations. It emphasizes the importance of understanding that absolute values cannot be negative, which leads to no solution scenarios. The tutorial aims to equip viewers with the skills to handle different types of absolute value equations effectively.

What is the absolute value of a number?

• The negative of the number

• The square of the number

• The number itself

• The distance from zero

In an absolute value equation, what does it mean if the equation has two solutions?

• The absolute value equals a negative number

• The absolute value equals a positive number

• The absolute value equals zero

• The equation is unsolvable

If the absolute value of x is 9, what are the possible values of x?

• Only 9

• 0

• 9 and -9

• Only -9

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

• Add a constant to both sides

• Isolate the absolute value

• Multiply both sides by a constant

• Subtract a constant from both sides

What does it mean if an absolute value equation has one solution?

• The absolute value equals a negative number

• The absolute value equals a positive number

• The equation has no solution

• The absolute value equals zero

If the absolute value of x equals zero, what is the value of x?

• x can be any number

• x is zero

• x is positive

• x is negative

Why can't an absolute value equation equal a negative number?

• Because absolute values are always positive or zero

• Because it would have no solutions

• Because negative numbers don't exist

• Because it would have infinite solutions

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

• It is undefined

• It has one solution

• It has two solutions

• It has no solution

In the equation |x| = -5, what can x be?

• 5

• -5

• Any number

• No solution

What is the key takeaway about absolute value equations?

• They never have solutions

• They always equal zero

• They can have two, one, or no solutions

• They always have two solutions