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 < -5 or x > 5 represent on a number line?

Back

It represents two separate regions on the number line: all numbers less than -5 and all numbers greater than 5.

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 inequality 2 ≤ x ≤ 4?

Back

You graph it by shading the region between 2 and 4 on the number line, including the endpoints.

Front

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

Back

The solution is x < -3.

Front

What does the inequality -4x + 5 < 1 simplify to?

Back

It simplifies to x > 1.

Front

How do you write an inequality for a given graph?

Back

Identify the endpoints and the direction of shading to write the corresponding inequality.

Front

What is the solution to the compound inequality x + 8 < 3 or -8x < -40?

Back

The solution is x < -5 or x > 5.

Front

What does the notation -2 ≤ x ≤ 5 indicate?

Back

It indicates that x is greater than or equal to -2 and less than or equal to 5.