Absolute Value Inequalities

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

Separate into two inequalities: -a < x < a.

Front

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

Back

Separate into two inequalities: x < -a or x > a.

Front

What is the first step to solve |x + 4| - 8 > 2?

Back

Add 8 to both sides to isolate the absolute value: |x + 4| > 10.

Front

What does the solution x > 6 or x < -14 represent in terms of a number line?

Back

It represents all numbers greater than 6 and all numbers less than -14.

Front

What is the first step to solve | -8x | < 8?

Back

Separate into two inequalities with an 'and': -8 < -8x < 8.

Front

What is the solution to the inequality |x + 3| > 8?

Back

x > 5 or x < -11.

Front

What does the term 'inequality' mean in mathematics?

Back

An inequality is a mathematical statement that indicates one quantity is larger or smaller than another, using symbols like <, >, ≤, or ≥.

Front

What is the difference between 'and' and 'or' in absolute value inequalities?

Back

'And' is used when the solution is within a range (e.g., |x| < a), while 'or' is used when the solution is outside a range (e.g., |x| > a).

Front

How do you graph the solution of an absolute value inequality?

Back

Use open circles for 'or' solutions and closed circles for 'and' solutions, shading the appropriate regions.