The big picture
Here is the whole track, in one table.
| Idea | What it means |
|---|---|
| A balance | = says both sides are the same number. |
| Expression or equation | No =: expression. = with both sides: equation. |
| Is this the one? | Put a number in. Both sides must match. |
| Undo an add | Add or take away the same number on both sides. The solution stays. |
| Undo a multiplication | Share both sides by the number in front of the letter. |
| Two steps | Undo the last step first. |
| From words | What repeats goes with the letter. Once stands alone. |
| Check it back | Put the answer into the first equation. |
| Both sides | Take the smaller number of k's off both sides. If the counts differ, k then sits on one side. |
| A bracket | Share both sides by the number outside. It cannot be 0. Or multiply it into every part of the bracket. Either way the answer stays. |
| No number fits | If both sides hold equal numbers of k's, take them off. Plain numbers that differ: no number fits. Plain numbers that match: every number fits. |
| The first slip | A line whose answer differs from the line before is wrong. The first such line is the slip. |
Your textbook calls this Part II, Chapter 7, Finding the Unknown. Go and try its questions.
An equals sign says two sides match. Keep them matching while one side gets simpler.