The Singing Hedgehog Guide to:
Algebra - Equations 5

Some examples where things often go wrong:
1.    negative answers
Solve the equation 4a + 6 = 2

What do we want it to say? We want it to say "a equals the answer"
What's in the wrong place? The plus 6
How do we get rid of it? We take away 6 from sides
 
4a + 6 = 2 becomes:
      4a = -4    standard wrong answer is 4a = 8
  so  a = -1

2a.    fractions
Solve the equation b/4 = 8

What do we want it to say? We want it to say "b equals the answer"
What's in the wrong place? The divide by 4; "fractions is division ... "
How do we get rid of it? We times by 4
 
    b/4 = 8 becomes:
         b = 32    standard wrong answer is b = 2
The question is often set up for the error like this with eight nicely divisible by four.

2b.    more fractions!
Solve the equation c/4 + 1/2 = 5/8

What do we want it to say? We want it to say "c equals the answer"
What's in the wrong place? All the fractions! We'll "cheat and change it"
How do we get rid of them? Carefully times everything by the LCM which is 8.
 
c/4 + 1/2 = 5/8  becomes:
     2c + 4 = 5
            2c = 1
            c = 1/2

3.    brackets
Solve the equation 4(2d - 3) = 4

What do we want it to say? We want it to say "d equals the answer"
What's in the wrong place? The brackets; BIDMAS applies here too
How do we get rid of them? We times everything inside by the number outside
 
4(2d - 3) = 4 becomes:
   8d - 12 = 4 
         8d = 16
           d = 2

4.    wrong way round
Solve the equation 4e + 6 = 7e

What do we want it to say? We want it to say "e equals the answer"
What's in the wrong place? There are too many e's on the right
How do we get rid of them? We swap everything over
 
4e + 6 = 7e becomes:
      7e = 4e + 6
      3e = 6
        e = 2 
 
5.    harder fractions
Solve the equation:
5f - 3 = 2
2f + 1

What do we want it to say? We want it to say "f equals the answer"
What's in the wrong place? The divide by 2f + 1
How do we get rid of it? We times by 2f + 1
basically the bottom on one side goes to the top on the other
 
5f - 3 = 2    becomes:
2f + 1   

5f - 3 = 2(2f + 1)    multiply the brackets
5f - 3 = 4f + 2        minus 3 in the wrong place, so add 3
     5f = 4f + 5        4f in the wrong place, so take away 4f
       f = 5

Now you need to practise:

downloadable worksheet
(save this file then run it)         
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