Question

How do you solve `6x + 9= 39`?

Answer 1

`x = 5`

Explanation:

Take the following steps to isolate and solve for `x` while keeping the equation balanced.

Subtract `9` from each side of the equation:

`6x + 9 - 9 = 39 - 9`

`6x + 0 = 30`

`6x = 30`

Divide each side of the equation by `6`

`(6x)/6 = 30/6`

`1x = 5`

`x = 5`

Answer 2

`x=5`

Explanation:

Using first principles:
Note that shortcut method derived from this approach.

Given:`" "color(green)(6x+9" "=" "39)`

Subtract `color(red)(9)` from both sides

`color(green)(6x+9color(red)(-9)" "=" "39color(red)(-9))`

`color(green)(6x+0=30)`

Divide both sides by `color(red)(6)`
Note that `-:6" is the same as "xx1/6`

`color(green)(6/(color(red)(6))xx x" "=" "30/(color(red)(6))`

`1xx x" "=" "5`

`x=5`
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`color(blue)("Footnote")`

From the above solution you observe the following:

`color(brown)("Point 1 - dealing with multiply or divide")`

To move the 6 from `6x` to the other side of the equals we changed it into 1. Thus for any number in multiply change it into 1.
Note that if you had `1/6x` it is still multiply as you have `1/6xx x` so you need to change `1/6` into 1
.............................................................................................................

`color(brown)("Point 2 - dealing with add or subtract")`

To move the constant 9 to the other side of the equals we changed it to 0. Thus for any constant you change it into 0. This is true for both plus and minus