Solving & Graphing 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 'or' mean in compound inequalities?

Back

In compound inequalities, 'or' indicates that at least one of the inequalities must be true for the solution to be valid.

Front

What does 'and' mean in compound inequalities?

Back

In compound inequalities, 'and' indicates that both inequalities must be true for the solution to be valid.

Front

How do you solve the compound inequality 3x + 2 < -4 or 4x + 4 > 24?

Back

x < -2 or x > 5.

Front

How do you solve the compound inequality 0 < x + 7 < 9?

Back

-7 < x and x < 2.

Front

What is the solution to the compound inequality 3x - 4 < -13 or 7x + 1 > 22?

Back

x < -3 or x > 3.

Front

How do you write an inequality for a graph showing x ≤ -2 or x > 5?

Back

x ≤ -2 or x > 5.

Front

What is the graphical representation of x < -2 or x > 5?

Back

Two separate regions on the number line: one to the left of -2 and one to the right of 5.

Front

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

Back

'x < a' means x is less than a, while 'x ≤ a' means x is less than or equal to a.

Front

What is the solution set for the inequality x > 3?

Back

The solution set includes all real numbers greater than 3.