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Linear inequalities in one or two variables
I worked these out from the practice questions. Each code says where to start reading, where to stop, what you can skip, and why it is safe.
1. Negative divide: flip
- Start:
- The step where you divide by the coefficient of x
- Stop:
- When you flip the sign for a negative
- Skip:
- The rest of the equation
- Why:
- Questions 3 and 7 both need a flip.
Used in questions 3, 7
2. Boundary tests
- Start:
- The boundary number in the answer choices
- Stop:
- After you test it with ≤ or <
- Skip:
- Everything far from the boundary
- Why:
- Questions 1 and 2 are decided by whether the boundary is included.
Used in questions 1, 2
3. Maximum? Round down
- Start:
- The sentence that says most, least or greatest
- Stop:
- When the number is whole
- Skip:
- The decimals
- Why:
- Rounding down for a maximum is the safe move (question 4).
Used in question 4
4. Test the points
- Start:
- The options for the system
- Stop:
- When one option passes both
- Skip:
- The remaining options
- Why:
- Put each option in both inequalities; a point must pass both (question 5).
Used in question 5
5. Do all three parts
- Start:
- The compound inequality
- Stop:
- After you list the integers
- Skip:
- Splitting it
- Why:
- Do the same steps on all three parts (question 6).
Used in question 6
6. Word to sign
- Start:
- The key words in the story
- Stop:
- When you pick ≤ or ≥
- Skip:
- Backstory
- Why:
- At least means ≥, at most means ≤ (questions 4 and 8).
Used in questions 4, 8
7. Desmos: graph the boundary
- Start:
- The inequalities
- Stop:
- When you see the shaded region
- Skip:
- Hand checks
- Why:
- Type the inequality in Desmos; it shades the region and you click your option (questions 5 and 6).
Used in questions 5, 6
8. Number line: circle type, then arrow
- Start:
- The circle on the number line
- Stop:
- When you name the sign from the circle and the arrow direction
- Skip:
- The scale numbers away from the circle
- Why:
- Open circle means strict (> or <), filled circle means ≥ or ≤. Arrow right means greater (question 9).
Used in question 9
9. Whole-number answers: test the boundary integers
- Start:
- The number your algebra gives, such as 75.33 or −5.5
- Stop:
- When you have tested the two whole numbers next to it
- Skip:
- Rounding by feel
- Why:
- Rounding the wrong way is the trap. Check the nearest whole numbers in the original inequality (questions 14 and 16).
Used in questions 14, 16
10. Shaded graph: line style, then test (0, 0)
- Start:
- The boundary line, solid or dashed
- Stop:
- When your test point agrees with the shading
- Skip:
- Re-deriving the shading by feel
- Why:
- Solid means the sign includes equals; dashed means it does not. Then test a point to know above or below (questions 11 and 15).
Used in questions 11, 15