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

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

Answered by FilupSmith last updated on 27/May/16

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

Commented by FilupSmith last updated on 27/May/16

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

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

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

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