2.8 Warmup

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable expression. It expresses the distance of the variable from a certain value on the number line.

Front

How do you solve the absolute value inequality |x + 3| > 4?

Back

To solve |x + 3| > 4, split it into two cases: x + 3 > 4 or x + 3 < -4. This leads to x > 1 or x < -7.

Front

What does the solution x < -7 or x > 1 represent on a number line?

Back

It represents all values of x that are either less than -7 or greater than 1, indicating two separate regions on the number line.

Front

What is the graphical representation of the inequality |x + 3| > 4?

Back

The graph consists of two rays: one extending left from -7 and the other extending right from 1.

Front

What is the first step in solving an absolute value inequality?

Back

The first step is to isolate the absolute value expression on one side of the inequality.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a means x is within a distance a from 0, while |x| > a means x is outside that distance.

Front

What does the term 'absolute value' mean?

Back

Absolute value refers to the distance of a number from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you express the solution of |x + 3| < 4?

Back

The solution is expressed as -4 < x + 3 < 4, which simplifies to -7 < x < 1.

Front

What is the significance of the number 4 in the inequality |x + 3| > 4?

Back

The number 4 represents the threshold distance from -3 that x must exceed to satisfy the inequality.

Front

What are the two cases to consider when solving |x + 3| < 4?

Back

The two cases are: x + 3 < 4 and x + 3 > -4.