2.5: SOLVING EQUATIONS: ABSOLUTE VALUE

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How many solutions does the equation |c - 7| = 2 have?

Back

Two solutions: c - 7 = 2 or c - 7 = -2, which gives c = 9 or c = 5.

Front

How many solutions does the equation 4|m| = -20 have?

Back

No solution, because the absolute value cannot be negative.

Front

How many solutions does the equation |-5c| = 0 have?

Back

One solution: -5c = 0, which gives c = 0.

Front

How many solutions does the equation -4 = |-6v| - 4 have?

Back

One solution: |-6v| = 0, which gives v = 0.

Front

Back

b = 18.

Front

Back

b = -36.

Front

What is the general form of an absolute value equation?

Back

An absolute value equation is typically in the form |x| = a, where a is a non-negative number.

Front

What does it mean if an absolute value equation has no solution?

Back

It means that the equation results in a contradiction, such as |x| = -a, where a is positive.

Front

What is the solution set for the equation |x| = a?

Back

The solution set is {a, -a}.