solving 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 signify?

Back

The 'AND' signifies that both conditions must be true at the same time.

Front

What does the 'OR' in a compound inequality signify?

Back

The 'OR' signifies that at least one of the conditions must be true.

Front

How do you solve the compound inequality 0 < x + 7 < 9?

Back

Subtract 7 from all parts: -7 < x < 2.

Front

What is the solution set for the inequality p ≤ 50?

Back

The solution set includes all values of p that are less than or equal to 50.

Front

How do you graph the inequality -5 ≤ x < 0?

Back

Use a closed dot at -5 and an open dot at 0, shading the region between them.

Front

What is the solution for the inequality x ≥ -2 AND x < 5?

Back

The solution set includes all values of x that are greater than or equal to -2 and less than 5.

Front

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

Back

Shading that always connects the two dots.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ includes the endpoint in the solution set, while < does not.

Front

How do you write the inequality for the graph showing all values from -2 to 5, including -2 but not 5?

Back

The inequality is -2 ≤ x < 5.