Question

Question #a6e1c

Answer 1

-31

Explanation:

`0.4(2x+0.5)=3(0.2x-2)`

Distribute on both sides

`0.8x+0.2=0.6x-6`

Move all x's to left side and all constants to right

`0.2x=-6.2`

Divide by 0.2 on both sides

x = -31

Answer 2

`x=-31`

Explanation:

Note that `0.4 ->4/10` and that `+(-2)->-2`

Write as `4/10(2x+1/2) = 3(0.2x-2)`

Getting rid of the 10 from `4/10` multiply both sides by 10

`4(2x+1/2)=30(color(white)(".")0.2x-2color(white)("."))`

Changing the `0.2` in the right bracket to `2/10`

`4(2x+1/2)=30(color(white)(".")2/10x-2color(white)("."))`

Multiply everything inside the bracket by what is outside

`8x+2color(white)("dd")=color(white)("dd")6x-60`

Subtract `color(red)(6x)` from both sides

`color(green)(8xcolor(red)(-6x)+2color(white)("dd")=color(white)("dd")6xcolor(red)(-6x)-60)`

`color(white)("dd")2xcolor(white)(".d")+2color(white)("dd")=color(white)("dddd")0color(white)("d.d")-60`

Subtract 2 from both sides

`2xcolor(white)("d")=color(white)("d")-62`

Divide both sides by 2

`color(green)(2/color(red)(2) x color(white)("d")=color(white)("d")-62/color(red)(2))`

`x=-31`