Question

How do I solve `3x + 6 = 9`?

Answer 1

`x=1`

Explanation:

First of all I will use the shortcuts. After that I will show what is actually happening. This will help in all sorts of ways.

`color(blue)("Short cut method")`

Move the 6 to the other side of the = and change its sign giving:

`3x =9-6`
`3x=3`

Move the three to other side of the = sign
Because it is multiply on the left it becomes divide on the right

`x= 3 divide 3`
`x=1`

`color(blue)("Now the explanation")`
The best way is to explain it as I go along

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Step 1.")`
Get just the x-terms on the left. In this case there is only 1
and that is `3x`.

Subtract 6 from both sides

`(3x+6 ) -6 = (9) -6`

but +6 and -6 is 0 giving

`3x+0 =9-6`

but 9-6 is 3 giving

`3x=3`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Step 2.")`
Now lets get rid of the 3 in `3x`
Note that `3x` is in fact `3 times x`

Divide both sides by 3 giving

`(3 times x) divide 3 = (3) divide 3`

But `divide 3` is the same as `times 1/3`

`(3 times x) times 1/3 = (3) times 1/3`

`3/3 times x = 3/3`

but `3/3` is 1 giving

`1 times x = 1`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 times anything is itself so `1 times x` is `x`

`color(blue)("And we have our answer of "x=1)`