Absolute Value Equations and Extraneous Solutions

Solve the following.

|3x + 4| = 10

Which of the following is the solution set?

• {2, -14/3}

• {-2, 14/3}

• No solution

• { }

We always check our solutions becasue there might be ____________________ solutions.

• funny

• correct

• extraneous

We always check our solutions because there might be ____________________ solutions.

• incorrect

• multiple

• extraneous

| x – 3 |= 0

• 3

• -3

• {-3, 3}

• no solution

A(n) __________________ is an equation that contains absolute value expressions.

• absolute value equation

• linear equation

• quadratic equation

• exponential equation

A(n) _____________________ solution is an apparent solution that must be rejected because it does not satisfy the original equation.

• extraneous

• double

• exponential

• progressive

TRUE or FALSE: It is possible for absolute value equations to have two solutions.

• True

• False

• 5 and - 5 

• 45 and - 45 

• 12 and - 12 

• 18 and - 18 

Does the equation given have a solution?

• Yes it will because we have to isolate the absolute value first

• No it will not because the right side is equivalent to a negative number 

|-2 - 4n| = 34

• n = -9, n = 8

• n = 9, n = 8

• n = -9

• n = 8