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 measures the distance of a number from zero on the number line.

Front

How do you solve the absolute value inequality |x - a| < b?

Back

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

Front

How do you solve the absolute value inequality |x - a| > b?

Back

To solve |x - a| > b, you split it into two inequalities: x < a - b or x > a + b.

Front

What does the solution to |x - 2| > 3 represent?

Back

The solution represents all values of x that are more than 3 units away from 2 on the number line.

Front

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

Back

'And' is used when the solution is a range between two values, while 'or' is used when the solution includes values outside a certain range.

Front

Solve the inequality: |x + 1| < 4.

Back

-5 < x < 3.

Front

Solve the inequality: |x - 3| > 2.

Back

x < 1 or x > 5.

Front

What is the graphical representation of |x - 2| < 3?

Back

It is represented as an open interval (2 - 3, 2 + 3) or (-1, 5) on the number line.

Front

What does the inequality |x| < a mean?

Back

It means that x is within a distance of a from 0, or -a < x < a.

Front

What does the inequality |x| > a mean?

Back

It means that x is more than a distance of a from 0, or x < -a or x > a.