Solving Compound Inequalities (2.11.2)

Question 1

• A compound inequality consists of two inequalities linked by a connective word, “and” or “or.”

Answer 1

• A compound inequality consists of two inequalities linked by a connective word, “and” or “or.”

Question 2

• “And” means that both inequalities must be satisfied at the same time. This relationship is sometimes called the intersection
where both inequalities hold true.

Answer 2

• “And” means that both inequalities must be satisfied at the same time. This relationship is sometimes called the intersection
where both inequalities hold true.

Question 3

• Graphing both solutions on a number line is the easiest way to see the intersection, or the entire range where both inequalities
hold true.

Answer 3

• Graphing both solutions on a number line is the easiest way to see the intersection, or the entire range where both inequalities
hold true.

Question 4

• “Or” means that either inequality must be satisfied, not necessarily both. This relationship is called a union because it can
be said to unite the two sets of solutions.

Answer 4

• “Or” means that either inequality must be satisfied, not necessarily both. This relationship is called a union because it can
be said to unite the two sets of solutions.

Question 5

• The term empty set indicates that there are no numbers which satisfy the terms of the compound inequality.

Answer 5

• The term empty set indicates that there are no numbers which satisfy the terms of the compound inequality.

Question 6

For this compound inequality, we want to see all the
numbers that satisfy both expressions.
On the number line we can see the two separate sets of
solutions. The set that works for both inequalities is clearly
all the numbers larger than –1 that are smaller than +2; i.e.,
–1 x > 5.
The word “and” asks for all the numbers that satisfy both
inequalities.
There are none.
So your solution is an empty set.

Answer 6

For this compound inequality, we want to see all the
numbers that satisfy both expressions.
On the number line we can see the two separate sets of
solutions. The set that works for both inequalities is clearly
all the numbers larger than –1 that are smaller than +2; i.e.,
–1 x > 5.
The word “and” asks for all the numbers that satisfy both
inequalities.
There are none.
So your solution is an empty set.