GCSE(F), GCSE(H),

A **linear equation** has numbers, including an unknown number, that are related to each other with an equals sign.

The equation may need to be **solved**, to find the value of the unknown number.

The equation can be seen as a seesaw which must *always* be balanced, with the equals sign being the fulcrum:

The golden rule is *if you do something to one side, you must do it to the other*.

The arithmetic is normally carried out by starting with the *least powerful* **BIDMAS** operations first, taking additional care where brackets are involved.

1. Solve `5y + 7 = 22`.

Answer: `y = 3`

`5y + 7 = 22` (first, subtract 7 from both sides)

`5y=15` (then, divide both sides by 5)

`y=3`

Check `5(3)+7=22`, which is true, so the answer is correct.

2. Solve `3(a+4)=6`.

Answer: `a=-2`

`3(a+4)=6` (expand brackets: see multiplying out brackets)

`3a + 12 = 6` (then subtract 12 from both sides)

`3a=-6` (next, divide both sides by 3)

`a=-2`

Check: 3((-2) + 4) = 6, which is correct.

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