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$$\mathbf{Solve}\frac{x+826}{x+2065}= 0.41\space \mathbf{FOR}\space x$$ Ok I came across this question in a GCSE paper and have no idea how to solve it. Please can you show me how one might go about working this out.

Thankyou,

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If we multiply both sides by the denominator $x+2065$, we have:

$$x+826=0.41(x+2065)=0.41x + 846.65$$

We can subtract $0.41x$ from both sides to give:

$$0.59x+826=846.65 \implies 0.59x=20.65 \implies x=\frac{20.65}{0.59}=35$$

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Does this help?

$$ x + 826 = .41x + 2065*.41?$$

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