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Answer 1 · 2017-10-29T21:22:11

-31

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

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 · 2017-10-29T21:37:58

$x=-31$

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

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

$x=-31$