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 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

What does the solution x < -3 or x > 1 represent on a number line?

Back

It represents all values of x that are either less than -3 or greater than 1, which are two separate regions on the number line.

Front

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

Back

In 'and' inequalities, the solution must satisfy both conditions simultaneously, while in 'or' inequalities, the solution can satisfy either condition.

Front

How do you graph the solution of a compound inequality?

Back

To graph the solution, plot the solutions of each inequality on a number line, using open or closed circles based on whether the endpoints are included.

Front

What is the solution to the inequality 3x + 2 < -7?

Back

The solution is x < -3.

Front

What is the solution to the inequality -4x + 5 < 1?

Back

The solution is x > 1.

Front

How do you write an inequality for a given graph?

Back

Identify the regions represented in the graph and express them as inequalities based on the endpoints and direction of the shading.

Front

What does the inequality x ≤ -2 OR x > 5 indicate?

Back

It indicates that x can be any value less than or equal to -2 or any value greater than 5.

Front

How do you solve the inequality x + 8 < 3?

Back

Subtract 8 from both sides to get x < -5.