Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

What does the symbol |x| < a represent?

Back

The symbol |x| < a means that the value of x is within a distance of a from zero, resulting in the compound inequality -a < x < a.

Front

What does the symbol |x| > a represent?

Back

The symbol |x| > a means that the value of x is outside the distance of a from zero, resulting in the compound inequality x < -a or x > a.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, often connected by the words 'and' or 'or'.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' indicates that both conditions must be true simultaneously, while 'or' indicates that at least one of the conditions must be true.

Front

How do you solve the inequality |x - 5| < 3?

Back

To solve |x - 5| < 3, you set up the compound inequality: -3 < x - 5 < 3, which simplifies to 2 < x < 8.

Front

How do you solve the inequality |2x + 1| > 4?

Back

To solve |2x + 1| > 4, you set up the compound inequalities: 2x + 1 < -4 or 2x + 1 > 4, which simplifies to x < -2.5 or x > 1.5.

Front

What is the graphical representation of |x| < a?

Back

The graphical representation of |x| < a is an open interval on the number line from -a to a, excluding the endpoints.

Front

What is the graphical representation of |x| > a?

Back

The graphical representation of |x| > a consists of two rays extending from -∞ to -a and from a to ∞, excluding the interval between -a and a.

Front

What is the first step in solving an absolute value inequality?

Back

The first step is to isolate the absolute value expression on one side of the inequality.