Cogito
Algebra 1 · Chapter 2 · Lesson 1
Solving Inequalities
One rule is different, and it matters.
10 problems · about 19 minutes · A-REI.B.3
What this lesson teaches
The student solves linear inequalities and explains why multiplying by a negative reverses the sign.
- Solve an inequality like an equation.
- Multiplying or dividing by a negative reverses the sign.
- The answer is a range, not a single value.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Absolute Value Equations: |x − 4| = 3. What is the larger solution?
Answer 7
Why 7.
Review — No Solution, or Every Solution: 8x + 2 = 8x + 11. How many solutions?
Answer 0
Why None.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSolve −2x ≥ 14. Boundary value?
Answer -7
Why x ≤ −7.
Why does the sign reverse with a negative?
Answer Multiplying by a negative reverses the order on the line.
Why The order on the line flips.
Solve 2x − 3 > 7. Boundary value?
Answer 5
Why 2x > 10.
Solve −3x < 12. Boundary value?
Answer -4
Why Reverse the sign.
Build It Up
The same ideas with more to keep track of.
2 problemsSolve 5x + 2 ≤ 27. Boundary value?
Answer 5
Why 5x ≤ 25.
Does dividing by a positive reverse the sign?
Answer No. Only a negative does.
Why The flip is about direction.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Range: Solve 3x + 4 < 19. What is the boundary value of x?
Answer 5
Why x < 5.
The Flip: Solve −4x > 20. What is the boundary value of x?
Answer -5
Why x < −5.