Absolute Value Inequalities practice

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| < a?

Back

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

Front

What does the inequality |x| > a represent?

Back

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

Front

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

Back

The graph of |x| < a is a line segment between -a and a on the number line.

Front

How do you express |x - 3| < 5 in terms of a compound inequality?

Back

|x - 3| < 5 can be expressed as -5 < x - 3 < 5, which simplifies to -2 < x < 8.

Front

What is the solution set for |x + 2| > 4?

Back

The solution set for |x + 2| > 4 is x < -6 or x > 2.

Front

How do you interpret the absolute value inequality |x| ≤ 7?

Back

The inequality |x| ≤ 7 means that x is between -7 and 7, inclusive.

Front

What is the difference between |x| < a and |x| ≤ a?

Back

|x| < a means x is strictly between -a and a, while |x| ≤ a includes the endpoints -a and a.

Front

How do you solve |2x - 4| < 6?

Back

To solve |2x - 4| < 6, split into -6 < 2x - 4 < 6, which simplifies to -2 < x < 5.

Front

What does the inequality |x - 1| > 3 indicate about x?

Back

The inequality |x - 1| > 3 indicates that x is either less than -2 or greater than 4.