Mastering Absolute Value Equations and Functions

What symbol is used to denote absolute value?

• Curly braces

• Vertical bars

• Square brackets

• Parentheses

How many solutions can an absolute value equation have?

• Three

• Up to two

• Infinite

• Only one

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

• Divide by the coefficient

• Add a constant

• Isolate the absolute value expression

• Set the equation to zero

What values of x solve the equation |x + 3| = 6?

• x = 3 and x = 9

• x = 0 and x = 9

• x = 3 and x = -9

• x = 6 and x = -6

After removing the absolute value bars, what should you do next?

• Multiply both sides by -1

• Factor the equation

• Combine like terms

• Solve the equation twice, once with a positive and once with a negative value

What is the purpose of setting the inside of the absolute value equal to both positive and negative values?

• To eliminate the absolute value

• To simplify the equation

• To ensure all possible solutions are considered

• To find the maximum solution

What is the solution to the equation |2x - 4| + 8 = 10?

• x = 3 and x = 1

• x = 4 and x = -4

• x = 2 and x = -2

• x = 5 and x = 0

How do you check if your solutions to an absolute value equation are correct?

• Consult the textbook

• Graph the equation

• Substitute the solutions back into the original equation

• Solve the equation again

What is the result of adding 4 to both sides of the equation |2x - 4| = 2?

• |2x| = 6

• |2x - 4| = 6

• |2x| = 2

• |2x - 4| = -2

What is a key takeaway when solving absolute value equations?

• They can only have positive solutions

• They always have a unique solution

• Isolating the absolute value expression is crucial

• They are solved like linear equations without modification