Question

0.2(6x+1)/3.6 = 0.5x/9

Answer 1

Answer:

x=-0.2

Step-by-step explanation:

The given equation is

$\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}$

We need to solve the given equation for x.

On cross multiplication we get

$9[0.2(6x+1)]=3.6(0.5x)$

$1.8(6x+1)=1.8x$

Using distribution property, we get

$1.8(6x)+1.8(1)=1.8x$

$10.8x+1.8=1.8x$

Subtract 1.8x and 1.8 from both sides.

$10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8$

$10.8x-1.8x=-1.8$

$9x=-1.8$

Divide both sides by 9.

$x=-\frac{1.8}{9}$

$x=-0.2$

Therefore, the value of x is -0.2.

Answer 2

The numbers are a bit ugly, but the equation can be solved as is.

... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left

... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions

... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator

... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18

... x = -1/5 . . . . . . . . . . . . . . . . divide by 5

_____

You can eliminate decimals and fractions by multiplying the given equation by 18.

... 6x +1 = x

... 5x +1 = 0

... 5x = -1

... x = -1/5

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The fraction simplification can work like this:

... 0.2/3.6 = 2/36 = 1/18

... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18