Solving & Graphing 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 graph a compound inequality with 'or'?

Back

To graph a compound inequality with 'or', you graph each inequality separately and then combine the graphs, showing all solutions.

Front

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

Back

To graph a compound inequality with 'and', you find the intersection of the solutions of the individual inequalities and graph that region.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to a specified number.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

Front

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

Back

To solve 0 < x + 7 < 9, subtract 7 from all parts to get -7 < x < 2.

Front

What is the solution set for the inequality x > 2 or x ≤ -3?

Back

The solution set includes all values greater than 2 and all values less than or equal to -3.

Front

How do you express the solution of the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

First, solve each inequality separately: -4x ≤ 20 gives x ≥ -5, and 5x < 20 gives x < 4. The solution is x ≥ -5 and x < 4.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

In 'and' inequalities, both conditions must be true simultaneously, while in 'or' inequalities, at least one condition must be true.

Front

How do you write an inequality for a given graph?

Back

To write an inequality for a graph, identify the boundary points and determine whether the graph includes or excludes those points (using <, >, ≤, or ≥).