DEVELOPING CONCEPTS
6.2
Investigating Inequalities
GOAL
Use reasoning to
determine whether
operations change an
inequality.
MATERIALS
• paper
• pencil
Question
For use with
Lesson 6.2
How do operations affect an inequality?
Write a true inequality by choosing two different numbers and placing the
appropriate symbol < or > between them.
Copy and complete the table. Apply the given rule to each side of your
inequality. Write the correct inequality symbol between the resulting numbers.
Original
inequality
Rule
Resulting
inequality
Did you have to
reverse the inequality?
?
Add 4.
?
?
?
Add 4.
?
?
?
Subtract 4.
?
?
?
Subtract 4.
?
?
?
Multiply by 4.
?
?
?
Multiply by 4.
?
?
?
Divide by 4.
?
?
?
Divide by 4.
?
?
Repeat Step 2 using different positive and negative integers.
Think About It
Using your results from Steps 2 and 3, predict whether the inequality
symbol will change when you apply the given rule. Check your prediction.
1. 4 < 9; add 7.
2. 15 > 12; subtract 5.
3. 4 > 3; multiply by 5.
4. 1 < 8; multiply by 10. 5. 6 < 2; divide by 3. 6. 0 < 8; divide by 2.
7. LOGICAL REASONING Copy and complete the table.
Must you reverse the inequality?
a positive number
a negative number
Add
?
?
Subtract
?
?
Multiply by
?
?
Divide by
?
?
Developing Concepts
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