Compound Absolute Value Inequalities (and/or)

Front

What is a compound absolute value inequality?

Back

A compound absolute value inequality combines two inequalities that involve absolute values, typically connected by 'and' or 'or'.

Front

What does the 'or' in a compound inequality indicate?

Back

The 'or' indicates that at least one of the inequalities must be true for the solution to be valid.

Front

What does the 'and' in a compound inequality indicate?

Back

The 'and' indicates that both inequalities must be true for the solution to be valid.

Front

How do you solve the inequality |x - 4| < 3?

Back

Split into two inequalities: x - 4 < 3 and x - 4 > -3, leading to the solution: 1 < x < 7.

Front

What is the first step in solving |2x + 12| < 8?

Back

Set up the two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

When graphing 'and' inequalities, how does the shading appear?

Back

The shading connects the two endpoints, indicating the overlap of the solutions.

Front

When graphing 'or' inequalities, how does the shading appear?

Back

The shading points away from the endpoints, indicating that solutions can be found in either direction.

Front

What is the solution to the inequality |x + 5| ≥ 2?

Back

Split into two inequalities: x + 5 ≥ 2 or x + 5 ≤ -2, leading to x ≥ -3 or x ≤ -7.

Front

What is the significance of the absolute value in inequalities?

Back

Absolute value measures the distance from zero, allowing for both positive and negative solutions.

Front

How do you determine if a compound inequality is 'and' or 'or'?

Back

Analyze the context: 'and' is used when both conditions must be satisfied, while 'or' is used when at least one condition must be satisfied.