Absolute Value Inequalities Review

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 the inequality |x - 2| < 7?

Back

To solve |x - 2| < 7, split it into two inequalities: -7 < x - 2 < 7, which simplifies to -5 < x < 9.

Front

What does the inequality |v| > 5 represent?

Back

The inequality |v| > 5 means that v is either greater than 5 or less than -5, represented as v > 5 or v < -5.

Front

What is interval notation for the inequality x > -1?

Back

The interval notation for x > -1 is (-1, ∞).

Front

How can the interval (-2, 12) be expressed in inequality notation?

Back

The interval (-2, 12) can be expressed in inequality notation as -2 < x < 12.

Front

What is the first step in solving the inequality 10|x| < 50?

Back

The first step is to divide both sides by 10, resulting in |x| < 5.

Front

What is the difference between 'AND' and 'OR' in compound inequalities?

Back

'AND' means both conditions must be true simultaneously, while 'OR' means at least one of the conditions must be true.

Front

How do you express the solution to |x| < a in interval notation?

Back

The solution to |x| < a is expressed in interval notation as (-a, a).

Front

What is the graphical representation of the inequality |x| > 3?

Back

The graphical representation of |x| > 3 consists of two rays: x < -3 and x > 3.

Front

What does it mean if an inequality is a compound inequality?

Back

A compound inequality involves two inequalities that are connected by 'AND' or 'OR', representing a range of values.