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Question Number 5782 by Rasheed Soomro last updated on 27/May/16

Why x+x=2x ? Explain by properties/laws.

$$\mathrm{Why}\:\mathrm{x}+\mathrm{x}=\mathrm{2x}\:\:? \\ $$$$\mathrm{Explain}\:\mathrm{by}\:\mathrm{properties}/\mathrm{laws}. \\ $$

Answered by FilupSmith last updated on 27/May/16

if you have a basket of x apples and i have an identical basket of x apples, we have 2 baskets of x apples so, 2x means two groups of x

$$\mathrm{if}\:\mathrm{you}\:\mathrm{have}\:\mathrm{a}\:\mathrm{basket}\:\mathrm{of} \\ $$$${x}\:\mathrm{apples}\:\mathrm{and}\:\mathrm{i}\:\mathrm{have}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{basket}\: \\ $$$$\mathrm{of}\:{x}\:\mathrm{apples},\:\mathrm{we}\:\mathrm{have}\:\mathrm{2}\:\mathrm{baskets}\:\mathrm{of}\:{x}\:\mathrm{apples} \\ $$$$ \\ $$$$\mathrm{so},\:\mathrm{2}{x}\:\mathrm{means}\:\mathrm{two}\:\:\mathrm{groups}\:\mathrm{of}\:{x} \\ $$$$ \\ $$

Commented by FilupSmith last updated on 27/May/16

multiplication is another form of writing additiom, essentially. 2x=x+x x^2 =x×x=x+x+...+x (x times) x^x =x×x×...×x (x times) =(x+x+...+x (x times)) {x times}

$$\mathrm{multiplication}\:\mathrm{is}\:\mathrm{another}\:\mathrm{form}\:\mathrm{of}\:\mathrm{writing} \\ $$$$\mathrm{additiom},\:\mathrm{essentially}. \\ $$$$ \\ $$$$\mathrm{2}{x}={x}+{x} \\ $$$${x}^{\mathrm{2}} ={x}×{x}={x}+{x}+...+{x}\:\:\:\:\:\left({x}\:\mathrm{times}\right) \\ $$$${x}^{{x}} ={x}×{x}×...×{x}\:\left({x}\:\mathrm{times}\right) \\ $$$$=\left({x}+{x}+...+{x}\:\:\:\left({x}\:{times}\right)\right)\:\left\{{x}\:{times}\right\} \\ $$

Answered by Rasheed Soomro last updated on 28/May/16

x+x=1×x +1×x [ 1 is multiplicative identity] =(1+1)×x [Right distributive law of ′×′ over ′+′ ] =2×x=2x

$$\mathrm{x}+\mathrm{x}=\mathrm{1}×\mathrm{x}\:+\mathrm{1}×\mathrm{x}\:\left[\:\mathrm{1}\:\mathrm{is}\:\mathrm{multiplicative}\:\mathrm{identity}\right] \\ $$$$=\left(\mathrm{1}+\mathrm{1}\right)×\mathrm{x}\:\left[\mathcal{R}{ight}\:\mathrm{distributive}\:\mathrm{law}\:\mathrm{of}\:\:\:'×'\:\:\mathrm{over}\:\:'+'\:\right] \\ $$$$=\mathrm{2}×\mathrm{x}=\mathrm{2x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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