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

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How do you graph the inequality 2 ≤ x ≤ 4?

Back

You graph it by drawing a number line, shading between 2 and 4, and using closed circles at 2 and 4.

Front

What is the solution set for the inequality x > 2 and x < 4?

Back

The solution set is the interval (2, 4).

Front

How do you write the inequality for the graph that shows x < -2 or x > 5?

Back

The inequality is written as x < -2 or x > 5.

Front

Is -2 a solution to the inequality -2x + 1 < 5?

Back

No, substituting -2 gives 5 < 5, which is false.

Front

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

Back

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

Front

How do you graph the inequality x > 2 or x ≤ -3?

Back

You graph it by shading to the right of 2 and shading to the left of -3.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only.