Understanding Absolute Value Equations

Msquared explains how to solve absolute value equations, emphasizing the importance of isolating the absolute value expression and checking for negative values. The video covers steps to solve these equations, provides examples, and highlights the concept that absolute values cannot be negative. It also demonstrates how to handle more complex equations and the importance of verifying solutions.

What does the absolute value of a number represent?

• The number itself

• The distance from zero

• The square of the number

• The negative of the number

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

• Add a constant to both sides

• Multiply both sides by a number

• Isolate the absolute value expression

• Subtract a constant from both sides

When writing two equations from an absolute value equation, what should you consider?

• The absolute value can only be positive

• The absolute value can be positive or negative

• The absolute value is always zero

• The absolute value can only be negative

Why can't an absolute value equation have a negative solution?

• Because absolute value represents distance, which is always positive

• Because numbers can't be negative

• Because negative numbers don't exist

• Because zero is the only negative number

What should you do if the right side of an absolute value equation is negative?

• Solve the equation as usual

• Multiply both sides by -1

• Ignore the negative sign

• Conclude that there is no solution

How do you eliminate multiplication when solving an absolute value equation?

• Multiply both sides by zero

• Divide both sides by the number

• Subtract the same number from both sides

• Add the same number to both sides

What is the result of dividing 24 by 4 in the context of solving an absolute value equation?

• 6

• 4

• 8

• 12

What should you always do after solving an absolute value equation?

• Ignore the solution

• Add 10 to the solution

• Multiply the solution by 2

• Check the solution in the original equation

If the absolute value of x minus 10 equals 5, what are the possible values of x?

• x = 10 or x = 0

• x = 15 or x = 5

• x = 5 or x = -5

• x = 20 or x = -20

What is the absolute value of -6?

• 6

• -6

• 0

• 12