Absolute Value Equations/Inequalites

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 do you solve an absolute value inequality of the form |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve an absolute value inequality of the form |x| ≥ a?

Back

To solve |x| ≥ a, split it into two inequalities: x ≤ -a or x ≥ a.

Front

What is the solution to the inequality |4v + 12| ≥ 6?

Back

v ≤ -4.5 or v ≥ -1.5.

Front

What is the solution to the inequality |x + 4| < 5?

Back

-9 < x < 1.

Front

How do you isolate the variable in an equation involving absolute value?

Back

Set the expression inside the absolute value equal to both the positive and negative of the other side of the equation.

Front

What is the solution to the equation |x - 6| + 4 = 10?

Back

x = 12 and x = 0.

Front

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

Back

It means that there are no values of the variable that can satisfy the equation.

Front

What is the solution to the equation -2|-2r - 4| = -12?

Back

{-5, 1}.

Front

What is the general form of an absolute value equation?

Back

An absolute value equation is typically in the form |A| = B, where A is an expression and B is a non-negative number.