Hello and welcome to the Linear Equations section of the ! To solve linear equations, you need to see the two sides of the equations as scales.

Then you need to find the unknown value. Linear equations come in a fantastic range of tasteless colours. Here are but a few...

1) 6x + 4 = 22

2) 22x + 6 = 16x - 30

3) 2 + x - 89 = 75

To solve number 1 you need to get rid of the 4 on the left-hand side (LHS) of the equation by subtracting it BUT...you need to subtract 4 on the right-hand side (RHS). When you've done this, you should end up with this:

6x = 18

(You guessed it...when you have a - sign, you add) Now then. To get x =(what you want), you need to divide the LHS and the RHS by 6. This reads:

6x/6 = 18/6

(Note: If you had 6x/6 = 18, you would just multiply both sides by 6) 6x/6 equals x (the two sixes cancel). 18/6 = 3. Therefore x = 3.

Right then, onto number 2.

22x + 6 = 16x - 30

Subtract 16x from both sides.

22x (- 16x) + 6 = 16x (- 16x) - 30

6x + 6 = - 30

Subtract 6 from both sides.

6x + 6 (- 6) = -30 (- 6)

6x = -36

Divide both sides by 6.

6x (/6) = -36 (/6)

x = - 6.

Get the examiner to put a big tick somewhere near your answer!

And finally... Number 3!

2 + x - 89 = 75

Add 89 to both sides.

2 + x - 89 (+ 89) = 75 (+ 89)

2 + x = 164

Subtract 2 from both sides

2 (- 2) + x = 164 (- 2)

x = 162

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