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

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

Back

The 'and' indicates that both conditions must be true at the same time.

Front

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

Back

The 'or' indicates that at least one of the conditions must be true.

Front

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

Back

You graph the overlapping region of the two inequalities.

Front

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

Back

You graph both inequalities separately, showing the regions where either condition is true.

Front

Solve the compound inequality: 3 < x < 7.

Back

The solution is all values of x between 3 and 7, not including 3 and 7.

Front

Write a compound inequality for the graph that shows x < -2 and x > 5.

Back

x < -2 or x > 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

Solve the compound inequality: -3 < x + 1 < 4.

Back

The solution is -4 < x < 3.

Front

What is the first step in solving a compound inequality?

Back

Isolate the variable in the middle of the inequality.