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The-number-of-values-of-x-which-are-satisfying-the-equation-x-4-8-x-x-4-is-where-Greatest-Integer-Function-

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Question Number 16086 by Tinkutara last updated on 17/Jun/17
The number of values of x which are satisfying the equation ∣x + 4∣ = 8[x] + x − 4 is? (where [∙] Greatest Integer Function)
Thenumberofvaluesofxwhicharesatisfyingtheequation∣x+4∣=8[x]+x−4is?(where[⋅]GreatestIntegerFunction)
Commented by prakash jain last updated on 17/Jun/17
∣x+4∣=8[x]+x−4 x≥−4 [x]+{x}+4=8[x]+[x]+{x}−4 8[x]=8⇒[x]=1 solution 1≤x<2 check x=1.5 5.5=8+1.5−4 x<−4 −(x+4)=8[x]+x−4 −x−4=8[x]+x−4 −2x=8[x] x=−4[x] [x]+{x}=−4[x] {x}=−5[x] no solution for x<−4 solution set1≤x<2
∣x+4∣=8[x]+x−4x⩾−4[x]+{x}+4=8[x]+[x]+{x}−48[x]=8⇒[x]=1solution1⩽x<2checkx=1.55.5=8+1.5−4x<−4−(x+4)=8[x]+x−4−x−4=8[x]+x−4−2x=8[x]x=−4[x][x]+{x}=−4[x]{x}=−5[x]nosolutionforx<−4solutionset1⩽x<2

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