Solve by trial and error, see why it can be slow, and learn that doing the same thing to both sides keeps an equation true.
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Try values, see if LHS = RHS, and move closer.
| n | LHS = 2n + 1 | Compared with 99 |
|---|---|---|
| 5 | 11 | far too low |
| 10 | 21 | too low |
| 30 | 61 | still low |
| 40 | 81 | closer |
| 50 | 101 | just too high |
| 49 | 99 | equal ✓ |
Trying to solve 5x − 4 = 7 by guessing.
Problem. Solve 5x − 4 = 7 by trial and error. (Textbook p. 168)
Solve by trial and error.
Solve 2n + 1 = 99.
Adding, subtracting, multiplying or dividing both sides by the same number keeps them equal.
Removing equal weights from both plates keeps a scale level. In the same way, doing the same operation to both sides of an equation keeps it true.
Check: 15 + 8 = 23. Add 10 to both sides: 15 + 8 + 10 = 33 and 23 + 10 = 33 ✓.
Examples 1–4: find part of a long calculation without working it out.
Problem. Use a known equality to find part of it. (Textbook pp. 169–170)
Use a known equality to find a part.
If A + 45 = 1000, then A = …