Compound Inequalities Review

Front

What is a compound inequality?

Back

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

Front

What does 'x > 2 and x < 4' represent?

Back

It represents the values of x that are greater than 2 and less than 4.

Front

How is '2 ≤ x ≤ 4' expressed in interval notation?

Back

[2, 4]

Front

What does 'x ≥ -2 or x < 5' mean?

Back

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

Front

What is the solution set for 'x < -2 or x > 5'?

Back

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

Front

How do you graph the inequality '2x + 10 ≤ 25'?

Back

First, solve for x: 2x ≤ 15, then x ≤ 7. Graph all values less than or equal to 7.

Front

What is the meaning of 'x ≤ -2 AND x > 5'?

Back

This compound inequality has no solution because no number can be both less than or equal to -2 and greater than 5.

Front

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

Back

'And' requires both conditions to be true, while 'or' allows for either condition to be true.

Front

How do you solve the inequality '2x + 10 > 20'?

Back

Subtract 10 from both sides: 2x > 10, then divide by 2: x > 5.

Front

What does the graph of 'x < 5' look like?

Back

A number line with an open circle at 5 and shading to the left.