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
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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
Answer:
x=-0.2
Step-by-step explanation:
The given equation is
[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]
[tex]1.8(6x+1)=1.8x[/tex]
Using distribution property, we get
[tex]1.8(6x)+1.8(1)=1.8x[/tex]
[tex]10.8x+1.8=1.8x[/tex]
Subtract 1.8x and 1.8 from both sides.
[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]
[tex]10.8x-1.8x=-1.8[/tex]
[tex]9x=-1.8[/tex]
Divide both sides by 9.
[tex]x=-\frac{1.8}{9}[/tex]
[tex]x=-0.2[/tex]
Therefore, the value of x is -0.2.
