Absolute Value Inequalities

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 + 3| > 8?

Back

Separate into two inequalities: x + 3 > 8 or x + 3 < -8, which simplifies to x > 5 or x < -11.

Front

What does the inequality | -8x | < 8 represent?

Back

It represents the values of x that are within 8 units of 0, leading to -8 < -8x < 8.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

Front

How do you represent the solution to |x - 4| ≤ 5?

Back

The solution is -1 ≤ x ≤ 9, meaning x is between -1 and 9, inclusive.

Front

What is the first step in solving |x + 2| < 6?

Back

Separate into two inequalities: x + 2 < 6 and x + 2 > -6.

Front

What does the solution r ≥ -38 and r ≤ 32 mean?

Back

It means r can take any value from -38 to 32, including the endpoints.

Front

How do you graph the inequality m < -1 OR m > 2?

Back

Draw a number line, shade to the left of -1 and to the right of 2, indicating that m can be in either region.

Front

What is the significance of the 'and' in absolute value inequalities?

Back

The 'and' indicates that both conditions must be true simultaneously, often leading to a range of values.

Front

What is the solution to the inequality |x| > 4?

Back

The solution is x < -4 or x > 4, meaning x is outside the interval [-4, 4].