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Question Number 124151 by mohammad17 last updated on 01/Dec/20

Answered by MJS_new last updated on 01/Dec/20

$$[ax+b]=\left[ax\right]+b$$$$\left(\mathrm{ii}\right)[x+3+[1+x+[x-2]]]=$$$$=[x+3+[1+x+\left[x\right]-2]]=$$$$=[x+3+[x+\left[x\right]-1]]=$$$$=[x+3+\left[x\right]+\left[x\right]-1]=$$$$=[x+2\left[x\right]+2]=$$$$=3\left[x\right]+2$$$$$$$$3\left[x\right]+2=5\Rightarrow \left[x\right]=1\Rightarrow 1⩽x<2$$$$\left(\mathrm{iii}\right)[3x+2]+[3x+7]=15$$$$2\left[3x\right]+9=15$$$$\left[3x\right]=3\Rightarrow 3⩽3x<4\Rightarrow 1⩽x<\frac{4}{3}$$

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