More on Compound Inequalities (2.11.3)

Question 1

• Remember to reverse the inequality if you multiply or divide by a negative number

Answer 1

• Remember to reverse the inequality if you multiply or divide by a negative number

Question 2

In this “or” example, our solution set will be all numbers
which satisfy either of the inequalities.
The best way to comprehend the total solution set is to graph
both sets on a number line.
A compound inequality can be written as one algebraic
sentence with two inequalities, as is the case here.
Solve it by changing all three sides in the same way until you
have a solution for x. This is easy so long as you are careful
with your arithmetic, your signs, and any inequality reversals
caused by multiplying with a negative number.
This is an “and” situation. We can consider the solution to
be ONLY those numbers that satisfy both unequal
relationships.

Answer 2

In this “or” example, our solution set will be all numbers
which satisfy either of the inequalities.
The best way to comprehend the total solution set is to graph
both sets on a number line.
A compound inequality can be written as one algebraic
sentence with two inequalities, as is the case here.
Solve it by changing all three sides in the same way until you
have a solution for x. This is easy so long as you are careful
with your arithmetic, your signs, and any inequality reversals
caused by multiplying with a negative number.
This is an “and” situation. We can consider the solution to
be ONLY those numbers that satisfy both unequal
relationships.