Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

How do you solve |x - a| < b?

Back

You create a compound inequality: a - b < x < a + b.

Front

How do you solve |x - a| > b?

Back

You create two inequalities: x < a - b or x > a + b.

Front

What does the symbol '|' represent in mathematics?

Back

The absolute value, which indicates the distance of a number from zero.

Front

What is the solution to |x| < c where c > 0?

Back

The solution is -c < x < c.

Front

What is the solution to |x| > c where c > 0?

Back

The solution is x < -c or x > c.

Front

What does 'and' mean in compound inequalities?

Back

Both conditions must be true simultaneously.

Front

What does 'or' mean in compound inequalities?

Back

At least one of the conditions must be true.

Front

How do you graph the solution of |x - 2| > 3?

Back

Graph the points x < -1 and x > 5 on a number line.

Front

What is the first step in solving 3|2x + 7| - 7 < -4?

Back

Add 7 to both sides to isolate the absolute value.