Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you graph the inequality x > 2?

Back

To graph x > 2, draw a number line, place an open circle at 2, and shade to the right.

Front

How do you graph the inequality x ≤ -3?

Back

To graph x ≤ -3, draw a number line, place a closed circle at -3, and shade to the left.

Front

What is the solution to the compound inequality x < -5 or x > 5?

Back

The solution includes all values less than -5 and all values greater than 5.

Front

What is the solution to the compound inequality -2 ≤ x ≤ 5?

Back

The solution includes all values of x from -2 to 5, including -2 and 5.

Front

How do you combine inequalities using 'and'?

Back

When combining inequalities using 'and', both conditions must be true for a solution to be valid.