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Lesson 15 of 16

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The table comes first, so you can look back at it. Then twelve checks.

Twelve ways of finding a hidden number
IdeaThe rule
Read the equals signThe beam lies flat only when both sides match.
Tell the two apartNo = waits. An = with both sides filled is a claim.
Test a numberWork each side out on its own. Same number both sides? That is the solution.
Undo an additionAdd or take away the same number on both sides.
Undo a multiplicationShare both sides by the number in front of the letter.
Two stepsUndo the last move first.
Read a puzzleWhat repeats takes the letter. What happens once stands alone.
Check it backPut the answer into the equation you started with.
Both sidesTake the smaller number of k's off both sides. If the counts differ, k then sits on one side.
A bracketShare 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 fitsIf 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 slipA 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?

  • Whenever the left pan holds longer writing
  • When both sides come to the same number
  • Whenever there is an equals sign between them

Which of these is an equation?

  • `9 + 8 = 17`
  • `2n + 5`
  • `7 + 4 =`

Is x = 4 the solution of x + 7 = 12?

  • Yes, because 4 is close to the answer
  • No — the equation has to be undone before any test
  • No — the left side comes to 11, the right side is 12

Take 7 off the left side of x + 7 = 12 only. What do you get?

  • `x = 5`, same as taking it off both sides
  • `x = 12`, which the original line was never true at
  • Nothing — that move is not allowed

What does sharing both sides of 5x = 45 by 5 give?

  • `x = 9`
  • `x = 225`
  • `5x = 9`

To solve 4x − 9 = 27, which first step undoes the 9?

  • Share both sides by 4
  • Take 9 off both sides
  • Add 9 to both sides

A shop charges ₹40 for a visit and ₹12 for each screw. The bill is ₹100. Which line says that?

  • `40s + 12 = 100`
  • `12s + 40 = 100`
  • `52s = 100`

Where do you put an answer back, to check it?

  • Into the equation you started with
  • Into the last line you wrote
  • Into whichever line has the letter alone

To solve 6m + 4 = 2m + 20, which move puts m on one side?

  • Add `2m` to both sides
  • Take 4 off both sides
  • Take `2m` off both sides

You solve 3(n + 5) = 36 two ways. First, share both sides by 3. Second, multiply 3 into the bracket. What do you find?

  • Both ways give `n = 7`
  • Only sharing first gives `n = 7`
  • The two ways give different answers

Which equation has no solution?

  • `4k + 2 = 3k + 8`
  • `5k + 6 = 5k + 9`
  • `7k + 1 = 2k + 1`

9w + 6 = 3w + 30 is solved as 6w + 6 = 30, then 6w = 30, then w = 5. Which is the first wrong line?

  • `w = 5`: it shows the wrong answer
  • `6w + 6 = 30`: `3w` is gone from both sides
  • `6w = 30`: the 6 came off the left side, not the right

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.

Reveal every answer to finish this lesson.

That is the end of this subject for Class 7

Nicely done. There is more waiting at this same level — pick whichever you like.