Solving Compound/Absolute Value Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

Define absolute value inequality.

Back

An absolute value inequality is an inequality that contains an absolute value expression, representing the distance from zero.

Front

What does the symbol '≤' mean?

Back

It means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

It means 'greater than or equal to'.

Front

How do you solve the inequality |x| < a?

Back

Split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

Back

Split it into two inequalities: x < -a or x > a.

Front

What is the solution set for the inequality -2x + 3 > -7?

Back

x < 5.

Front

What is the solution for the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

-1 ≤ x ≤ 3.

Front

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

Back

Identify the critical points and shade the appropriate regions based on the inequality.

Front

What does the solution x ≤ -2 OR x > 5 represent on a number line?

Back

It represents two separate regions: all values less than or equal to -2 and all values greater than 5.