Absolute Value Equations

Front

What is the definition of absolute value?

Back

The distance of a number from zero.

Front

True or False: The absolute value of a number can be negative.

Back

False, absolute value is always non-negative.

Front

Why is absolute value always expressed as a positive number?

Back

Because absolute value represents distance, which is always measured as a positive quantity.

Front

What is the solution set for the equation |x + 5| = 4?

Back

{ -1, -9 }.

Front

How do you solve the equation |x - 3| = 7?

Back

x = 10 or x = -4.

Front

What does the equation |x| = a imply when a is positive?

Back

x = a or x = -a.

Front

What is the solution to the equation |2x + 1| = 3?

Back

x = 1 or x = -2.

Front

If |x + 2| = 0, what is the value of x?

Back

x = -2.

Front

What is the graphical representation of an absolute value function?

Back

A V-shaped graph that opens upwards.

Front

How do you interpret the absolute value of a negative number?

Back

The absolute value of a negative number is its positive counterpart.