# Algebra - Worked Examples

## 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

### 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)

## 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

### 24 = a4 = 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)

### Order of Operations, BODMAS / BIDMAS

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