Solving Absolute Value Equations Challenge

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

• Add a constant to both sides

• Subtract a constant from both sides

• Divide both sides by a constant

• Multiply both sides by a constant

What do you do after isolating the absolute value expression?

• Break it into two separate equations

• Take the square root of both sides

• Combine like terms

• Square both sides

What are the two equations derived from |x + 1| = -18?

• x + 1 = -18 and x + 1 = 18

• x + 1 = 0 and x + 1 = 18

• x + 1 = -18 and x + 1 = -18

• x + 1 = 18 and x + 1 = 18

What are the solutions to the equations x + 1 = -18 and x + 1 = 18?

• x = -19 and x = 17

• x = -17 and x = 19

• x = -18 and x = 18

• x = -1 and x = 1

What happens when you plug x = -19 back into the original equation?

• You get an undefined result

• You get a negative result

• You get zero

• You get a positive result

Why is there no solution to the equation |x + 1| = -18?

• Because the variable is not isolated

• Because absolute values cannot be negative

• Because the constant is too large

• Because the equation is not linear

What should you do if you miss the special case and solve the equation anyway?

• Divide the solutions by a constant

• Ignore the solutions

• Check the solutions by plugging them back into the original equation

• Multiply the solutions by a constant

What is an extraneous solution?

• A solution that does not satisfy the original equation

• A solution that satisfies the original equation

• A solution that is a fraction

• A solution that is an integer

Why is it important to check your solutions in absolute value problems?

• To simplify the equation

• To find the maximum value

• To ensure they satisfy the original equation

• To eliminate negative values

What caused the negative value in the equation |x + 1| = -18?

• Dividing both sides by 22

• Subtracting 22 from both sides

• Adding 22 to both sides

• Multiplying both sides by 22