Algebra - Worked Examples

Let's look at a couple of examples to reinforce the process.

Rearrange, 10c - 2 = 7c + 4

We need to rearrange this equations so that all the letters are on one side of the equals sign and all the numbers are on the other

'Letters on one side and numbers on the other'

Which side of the equals sign you are going to have the letters - largest value is the side you keep the letters on - so letters on the left

Remove the numbers from the left side ... use the inverse operation ... inverse of -2 is + 2 ... 10c - 2 + 2

Do the same to both sides to keep the equation balanced
so add 2 to the right side ... 7c + 4 + 2

Remove the letters from the right side, use the inverse operation ...
inverse of 7c is - 7c ,,, 7c - 7c + 6

Do the same to both sides to keep the equation balanced
so subtract 7c from the left side ... 10c - 7c is 3c

We still have mixture of letters and numbers on the left ..... so
use the inverse operation again ... remember that 3c, really means 3 x c
The inverse of multiply is divide so divide by 3 ... 3 x c ÷ 3 is c

Do the same to both sides to keep the equation balanced
so divide 6 by 3 from the right side ... 6 ÷ 3 = 2

10c = 7c + 4

10c = 7c + 6

10c = 6

3c = 6

c = 6


c = 2

 

You should always check your result by putting your answer into the original equation

10c - 2 = 7c + 4    is    10 x 2 - 2 = 7 x 2 +4    is     18 = 18

(don't forget to do the multiplying first)

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Rearrange, 3a + 8 = 9a - 16

We need to rearrange this equations so that all the letters are on one side of the equals sign and all the numbers are on the other

'Letters on one side and numbers on the other'

Which side of the equals sign you are going to have the letters - largest value is the side you keep the letters on - so letters on right

Remove the numbers from the right side ... use the inverse operation ... inverse of -16 is + 16 ... 9a - 16 + 16

Do the same to both sides to keep the equation balanced
so add 16 to the left side ... 3a + 8 +16

Remove the letters from the left side, use the inverse operation ...
inverse of 3a is - 3a ... 3a - 3a

Do the same to both sides to keep the equation balanced
so subtract 3a from the right side ... 9a - 3a is 6a

We still have mixture of letters and numbers on the right ..... so
use the inverse operation again ... remember that 6a, really means 6 x a
The inverse of multiply is divide so divide by 6 ... 6 x a ÷ a is a

Do the same to both sides to keep the equation balanced
so divide 24 by 6 from the left side ... 24 ÷ 6 = 4

3a + 8 = 9a

3a + 24 = 9a

24 = 9a

24 = 6a

24 = a


4 = a

Check your result by putting your answer into the original equation

3a + 8 = 9a - 16    is    3 x 4 + 8 = 9 x 4 - 16    is    20 = 20

(don't forget to do the multiplying first)

Practice with these worksheets from Math Drills

    Simple Equations 1                      Simple Equations 2 

   Evaluating Equations                      Rewriting Equations

Algebra, Rearranging Equations  Order of Operations, BODMAS / BIDMAS  Order of Operations, BODMAS or BIDMAS

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