Cogito
Integrated Math 1 · Chapter 1 · Lesson 2
Inequalities
One rule behaves differently.
12 problems · about 20 minutes · A-REI.B.3
What this lesson teaches
The student solves and graphs linear inequalities, including compound ones.
- Solve an inequality like an equation, with one exception.
- Multiplying or dividing by a negative reverses the sign.
- Open circles exclude the endpoint; closed circles include it.
Warm Up
Straightforward practice. Get the method working first.
5 problems4x > 20. What is the boundary value for x?
Answer 5
Why 5, so x > 5.
When does an inequality sign reverse?
Answer When multiplying or dividing by a negative number.
Why Only multiplication or division by a negative.
x + 4 < 9. What is the boundary value for x?
Answer 5
Why Subtract 4.
2x ≥ 14. What is the boundary value?
Answer 7
Why Divide by 2.
−3x > 9. What is the boundary value?
Answer -3
Why Divide by −3 and flip.
Build It Up
The same ideas with more to keep track of.
3 problemsDoes dividing by −4 reverse the sign? 1 yes, 0 no.
Answer 1
Why Dividing by a negative flips it.
Does subtracting 6 reverse the sign? 1 yes, 0 no.
Answer 0
Why Only multiplying or dividing by a negative.
5x + 3 ≤ 23. What is the boundary value?
Answer 4
Why Subtract 3, then divide by 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each symbol by the circle it uses on a number line.
Answer Open circle: Less than, Greater than · Closed circle: Less than or equal to, Greater than or equal to
Why The endpoint is included only when "or equal to" appears.
−2x ≤ 10. What is the boundary value?
Answer -5
Why Divide by −2 and flip.
The Solve: 3x < 12. What is the largest whole number x can be?
Answer 3
Why 3.
The Budget: Items cost $7 each and you have $50. What is the most you can buy?
Answer 7
Why 7 items.