Absolute Value Inequalities #2

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

What does the inequality |x| < a represent?

Back

It represents all values of x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents all values of x that are more than a distance a from 0 on the number line.

Front

Solve the inequality |x - 2| < 5.

Back

-3 < x < 7.

Front

Solve the inequality |x + 4| ≥ 3.

Back

x ≤ -7 or x ≥ -1.

Front

What is the solution set for |x| < 2?

Back

The solution set is {x: -2 < x < 2}.

Front

What is the solution set for |x| > 3?

Back

The solution set is {x: x < -3 or x > 3}.

Front

Solve the inequality |2x + 1| ≤ 4.

Back

-2.5 ≤ x ≤ 1.5.

Front

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

Back

It is represented by an open interval on the number line from -a to a.

Front

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

Back

It is represented by two rays extending from -∞ to -a and from a to ∞.