Track quiz
The table comes first, so you can look back at it. Then twelve checks.
| Idea | The rule |
|---|---|
| Read the equals sign | The beam lies flat only when both sides match. |
| Tell the two apart | No = waits. An = with both sides filled is a claim. |
| Test a number | Work each side out on its own. Same number both sides? That is the solution. |
| Undo an addition | Add or take away the same number on both sides. |
| Undo a multiplication | Share both sides by the number in front of the letter. |
| Two steps | Undo the last move first. |
| Read a puzzle | What repeats takes the letter. What happens once stands alone. |
| Check it back | Put the answer into the equation you started with. |
| 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. |
A beam balance holds one side of an equation in each pan. When does it lie flat?
Which of these is an equation?
Is x = 4 the solution of x + 7 = 12?
Take 7 off the left side of x + 7 = 12 only. What do you get?
What does sharing both sides of 5x = 45 by 5 give?
To solve 4x − 9 = 27, which first step undoes the 9?
A shop charges ₹40 for a visit and ₹12 for each screw. The bill is ₹100. Which line says that?
Where do you put an answer back, to check it?
To solve 6m + 4 = 2m + 20, which move puts m on one side?
You solve 3(n + 5) = 36 two ways. First, share both sides by 3. Second, multiply 3 into the bracket. What do you find?
Which equation has no solution?
9w + 6 = 3w + 30 is solved as 6w + 6 = 30, then 6w = 30, then w = 5. Which is the first wrong line?
Your textbook calls this Part II, Chapter 7, Finding the Unknown. You have levelled a beam and undone steps. You have checked answers back.
An equals sign says two sides match. Keep them matching while one side gets simpler.