Absolute Value Inequalities 1

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

What does the symbol '|' represent in mathematics?

Back

The symbol '|' represents absolute value, which indicates the non-negative value of a number regardless of its sign.

Front

What is the general form of an absolute value inequality?

Back

The general form is |expression| < a or |expression| > a, where 'expression' is a mathematical expression and 'a' is a positive number.

Front

When solving |x| < a, what type of inequality is formed?

Back

A compound inequality of the form -a < x < a.

Front

When solving |x| > a, what type of inequality is formed?

Back

A compound inequality of the form x < -a or x > a.

Front

What does the solution to |x - 3| ≤ 5 represent on a number line?

Back

It represents all values of x that are within 5 units of 3, which is the interval [−2, 8].

Front

How do you isolate the absolute value in an inequality?

Back

To isolate the absolute value, you first manipulate the inequality to get the absolute value expression by itself on one side.

Front

What is the first step in solving the inequality 3|d - 4| ≥ 12?

Back

Divide both sides by 3 to isolate the absolute value: |d - 4| ≥ 4.

Front

What does the solution to the inequality -5|2x + 3| < -40 indicate?

Back

This inequality has no solution because the left side is always non-positive, while the right side is negative.

Front

What is the significance of the 'and' in compound inequalities involving absolute values?

Back

The 'and' indicates that both conditions must be satisfied simultaneously, typically seen in |x| < a.