1-3-24 Absolute Value Inequalities (Greater Than)

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

Front

How do you solve an absolute value inequality of the form |x| > a?

Back

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

Front

What is the first step in solving the inequality 7|7x - 7| > 49?

Back

Get the absolute value alone by dividing both sides by 7.

Front

What does the solution x < 0 or x > 2 represent on a number line?

Back

It represents all values of x that are either less than 0 or greater than 2, creating two separate regions on the number line.

Front

How do you graph the solution to an absolute value inequality?

Back

Graph the critical points found from solving the inequality and shade the appropriate regions based on the inequality sign.

Front

What is the solution to the inequality |3x + 3| > 12?

Back

x > 3 or x < -5.

Front

What does the inequality |x - 4| > 6 mean?

Back

It means that the distance between x and 4 is greater than 6, leading to two solutions: x < -2 or x > 10.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often connected by 'and' or 'or', representing a range of values.

Front

How do you interpret the solution m < -1 OR m > 2?

Back

It means that m can take any value less than -1 or any value greater than 2.

Front

What is the significance of the absolute value in inequalities?

Back

The absolute value indicates the magnitude of a number without regard to its sign, affecting how we interpret distances and ranges.