Question

How do you solve `3.2(6x-7.2) = 0`?

Answer 1

`x=1.2`

Explanation:

1. Apply distributive property `a(b+c)=a(b)+a(c)`
   `3.2(\color(crimson)(6x)\color(orchid)(-7.2))=0` becomes...
   `3.2(\color(crimson)(6x))+3.2(\color(orchid)(-7.2))=0`
2. Simplify by multiplication
   `\color(crimson)(19.2x)+(\color(orchid)(-23.04))=0`
   `19.2x-23.04=0`
3. Isolate the term with variable `x` using addition
   `19.2x\cancel(-23.04)\cancel(color(tomato)(+23.04))=0\color(tomato)(+23.04)`
   `19.2x=23.04`
4. Isolate the variable `x` by division
   `(\cancel(19.2)x)/(\cancel(\color(lightcoral)(19.2)))=23.04/(\color(lightcoral)(19.2)`
5. Here is your result!
   `x=1.2`

Answer 2

`x=18/15 = 1.2`

In the absence of any instruction your solution format is the same as in the question.

Explanation:

Given: `color(green)(3.2(6x-7.2)=0)`

Divide both sides by `color(red)(3.2)`

`color(green)(3.2(6x-7.2)=0color(white)("dddd")->color(white)("dddd")ubrace(3.2/color(red)(3.2)) (6x-7.2)=0/color(red)(3.2))`

`color(green)(color(white)("dddddddddddddddddd")->color(white)("ddddd")1xx( 6x-7.2)=0`

Add `color(red)(7.2)` to both sides

`color(green)(color(white)("dddd")6x-7.2=0color(white)("dddd") ->color(white)("ddddd")6xcolor(white)("d")ubrace(-7.2color(red)(+7.2)) = 0color(red)(+7.2)`

`color(green)( color(white)("dddddddddddddddddd") ->color(white)("ddddd")6xcolor(white)("d.d")+0color(white)("dddd")=7.2 )`

Divide both sides by `color(red)(6)`

`color(green)(color(white)("dddd")6x=7.2color(white)("ddddddd") ->color(white)("ddddd")6/color(red)(6) x=7.2/color(red)(6) )`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determined that `x=7.2/6` we find the decimal to be awkward. So we 'get rid of it!

`x=(7.2xx10)/(6xx10) = 72/60 = 36/30 = 18/15`