courses › Algebra

Solve inequalities and count the whole numbers that fit.

Pen and paper is fine · no calculator needed why?

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Opens at level 23.

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Builds on: Linear equations (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Solve an inequality par 15 s not tried yet

  worked example

  Solve for x: 3x + 7 < −17

  1. x < 8
  2. x < −8
  3. x > 8
  4. x > −8

  Answer: x < −8

  1. Subtract 7 from both sides: 3x < −24.
  2. Divide by 3; it is positive, so the sign stays: x < −8.

• Largest whole solution par 16 s not tried yet

  worked example

  What is the largest integer n with 3n − 13 < −24?

  Answer: -4

  1. Add 13 to both sides: 3n < −11.
  2. Divide by 3: n < −11/3, which is about −3.67.
  3. The largest integer that fits is −4.

• Count the solutions par 20 s not tried yet

  worked example

  How many integers x satisfy |x − 4| ≤ 2?

  Answer: 5

  1. |x − 4| ≤ 2 means −2 ≤ x − 4 ≤ 2, so 2 ≤ x ≤ 6.
  2. Count both ends: 6 − 2 + 1 = 5 integers.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

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