Solving Absolute Value Equations

What does the absolute value of a number represent?

• The square of the number

• The negative of the number

• The distance from zero

• The number itself

If the absolute value of ax + B equals C, and C is positive, what can we conclude?

• X must be zero

• There is no solution

• X must be negative

• X can be a solution

Why can't the absolute value of an expression be equal to a negative number?

• Because it can only be zero

• Because it depends on the variable

• Because negative numbers don't exist

• Because absolute values are always positive

What are the two possible equations derived from |x| = 8?

• x = 8 and x = -8

• x = 8 and x = 0

• x = 8 and x = 16

• x = 8 and x = -16

In the equation |x + 1| = 3, what are the two possible values of x?

• x = 2 and x = -2

• x = 2 and x = -4

• x = 4 and x = -4

• x = 3 and x = -3

What is the first step in solving |4x| + 2 = 14?

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 4

• Multiply both sides by 4

After isolating the absolute value in |4x| = 12, what are the two possible equations?

• 4x = 12 and 4x = -12

• 4x = 12 and 4x = 0

• 4x = 12 and 4x = 24

• 4x = 12 and 4x = -24

What are the solutions to the equation 4x = 12?

• x = 3 and x = 6

• x = 3 and x = 0

• x = 3 and x = -6

• x = 3 and x = -3

What should you do if there is a number outside the absolute value in an equation?

• Ignore it

• Multiply it by both sides

• Subtract it from both sides

• Add it to both sides

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

• Rewrite the equation

• Check the solutions

• State the solutions

• Graph the solutions