Solving Linear Equations

Solving Linear Equations

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:

linear equation seesaw

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.

Examples

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.