Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using the words 'and' or 'or'.

Front

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

Back

It means 'less than or equal to'.

Front

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

Back

It means 'greater than or equal to'.

Front

How do you represent the solution of the compound inequality -2 ≤ x ≤ 5 on a number line?

Back

Draw a line segment from -2 to 5 with closed dots at -2 and 5.

Front

What is the solution set for the compound inequality x < 1 and x > 5?

Back

No solution, as no number can be both less than 1 and greater than 5.

Front

What is the solution set for the compound inequality x < 1 or x > 5?

Back

The solution set includes all numbers less than 1 and all numbers greater than 5.

Front

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

Back

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

Front

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

Back

'And' requires both conditions to be true, while 'or' requires at least one condition to be true.

Front

When graphing the inequality x ≥ -2, what type of dot is used?

Back

A closed dot is used to indicate that -2 is included in the solution.

Front

What is the solution to the inequality 3x - 5 < 4?

Back

x < 3.