Solving Absolute Value Equations

What is an extraneous solution?

• A solution that is always positive.

• A solution that does not satisfy the original equation.

• A solution that satisfies the original equation.

• A solution that is always negative.

When solving an absolute value equation, what should you do after opening the absolute value symbol?

• Set the inside equal to the reciprocal of the outside.

• Set the inside equal to the square of the outside.

• Set the inside equal to zero.

• Set the inside equal to the positive and negative values of the outside.

What is the first step in solving the equation |2x + 5| = 6x - 7?

• Subtract 2x from both sides.

• Divide both sides by 4.

• Write two equations: one with the positive value and one with the negative value.

• Add 7 to both sides.

What is the potential solution for x when solving 2x + 5 = 6x - 7?

• x = 3

• x = 2

• x = 1

• x = 4

How do you verify if x = 3 is a solution to the equation |2x + 5| = 6x - 7?

• By substituting x = 3 into the original equation and checking if both sides are equal.

• By substituting x = 3 into the simplified equation.

• By checking if x = 3 is a positive number.

• By checking if x = 3 is a negative number.

What is the result of substituting x = 3 into the equation |2x + 5| = 6x - 7?

• Both sides equal 10.

• Both sides equal 11.

• Both sides equal 12.

• Both sides equal 13.

What is the potential solution for x when solving 2x + 5 = -6x - 7?

• x = 1/4

• x = 1/2

• x = 1

• x = 3/4

What is the first step in solving the equation |3x - 4| = 2x - 6?

• Add 4 to both sides.

• Subtract 2x from both sides.

• Write two equations: one with the positive value and one with the negative value.

• Divide both sides by 5.

What is the potential solution for x when solving 3x - 4 = 2x - 6?

• x = 0

• x = 1

• x = -2

• x = -1

What is the result of substituting x = -2 into the equation |3x - 4| = 2x - 6?

• Both sides equal -10.

• Both sides equal 10.

• Both sides equal -12.

• Both sides equal 12.