Solving 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

'AND' indicates that both conditions must be true simultaneously for a solution to be valid.

Front

What does 'OR' mean in a compound inequality?

Back

'OR' indicates that at least one of the conditions must be true for a solution to be valid.

Front

How do you graph a compound inequality with 'AND'?

Back

You graph the overlapping region of the two inequalities on a number line.

Front

How do you graph a compound inequality with 'OR'?

Back

You graph both inequalities separately, showing the entire range of values for each.

Front

What is the solution to the compound inequality x > 5 OR x < -2?

Back

The solution includes all values greater than 5 and all values less than -2.

Front

What is the solution to the compound inequality x ≤ -2 AND x > 5?

Back

There is no solution because no number can be both less than or equal to -2 and greater than 5.

Front

How do you solve the compound inequality 24 > -3r > -9?

Back

Divide the entire inequality by -3 (remember to flip the inequality signs): 8 < r < 3.

Front

What is the solution to the compound inequality 0 < x + 7 < 9?

Back

Subtract 7 from all parts: -7 < x < 2.

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.