# Algebra simplify question?

How would I simplify this?

$$5\% \cdot \frac12 \left(3000 + 2x\right)$$

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My book says it is 165+.11x but I am not sure how – James May 31 '12 at 18:02
First step: write the expression in symbols, then we can give you hints. – rschwieb May 31 '12 at 18:05

You have: $0.05\cdot0.5(3000+2x)=0.025\cdot(3000+2x)=75+0.05x$

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Assuming this is what you mean:
$$5\%*\frac{1}{2}*(3000+2x)$$
I assume you know that $5\%=\frac{5}{100}=\frac{1}{20}$. So we have
$$\frac{1}{40}*(3000+2x)=\frac{3000}{40}+\frac{2x}{40}=75+\frac{x}{20}$$

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If that's what the solution is supposed to be to your problem, it looks like the original problem should be

$$0.11\cdot\frac{1}{2}(3000+2x)$$

I would reduce this by distributing the 1/2 first: $$0.11(1500+x)$$ Then distribute the .11, using the trick $.11(1500)=.11(100)15=11(15)=165$ to get $$165+.11x$$

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