Question

How do you solve `13A = 65`?

Answer 1

`color(blue)(A=5`

Explanation:

`13A=65`

`A=65/13`

`color(blue)(A=5`

Answer 2

`A=65/13`

The explanation gives a very detailed introduction to the method for solving this type of question!

Explanation:

Given: `color(brown)(13A=65)`

`color(brown)("The objective is to get A on its own on one side of the equals sign")` `color(brown)("and everything else on the other.")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("There three things that it is very important you remember:")`

`color(blue)("Point 1:")`
If we can change the 13 from 13A into the value of 1 we
would have `1xxA` which is the same as just `A`.

`color(blue)("Point 2:")`
What you do to one side of the equals you also do the other.
Consider 4=4. This we know to be true. But suppose we subtracted 1 from only the left side we would have `4-1!=4` but if we did this instead; `4-1=4-1` then both sides still have the same value.
`color(white)(xxxx)`
`color(blue)("Point 3")`
The same process applies to addition, multiplication, division squaring, taking square roots and so on!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(brown)("Changing the 13 into 1")`

Multiply both sides by `color(blue)(1/13)`

`color(blue)(1/13xxcolor(brown)( 13A = 65)xx1/13)`

giving:

`13/13xxA=65/13`

`1xxA=65/13`

But `1xxA` is the same as just `A` giving

`A=65/13`