If y = 3[x] + 1 = 4[x - 1] - 10,then [x + 2y] | vedclass

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(C) Given the equation $y = 3[x] + 1 = 4[x - 1] - 10$.Using the property of the $Greatest$ $Integer$ $Function$ $[x - n] = [x] - n$ for any integer $n

Vedclass · Accepted Answer

$107$

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(C) Given the equation $y = 3[x] + 1 = 4[x - 1] - 10$.Using the property of the $Greatest$ $Integer$ $Function$ $[x - n] = [x] - n$ for any integer $n$,we have $[x - 1] = [x] - 1$.Substituting this into the equation:$3[x] + 1 = 4([x] - 1) - 10$$3[x] + 1 = 4[x] - 4 - 10$$3[x] + 1 = 4[x] - 14$Rearranging the terms to solve for $[x]$:$4[x] - 3[x] = 1 + 14$$[x] = 15$.Now,substitute $[x] = 15$ into the expression for $y$:$y = 3(15) + 1 = 45 + 1 = 46$.We need to find the value of $[x + 2y]$:$[x + 2y] = [x + 2(46)] = [x + 92]$.Since $92$ is an integer,we use the property $[x + n] = [x] + n$:$[x + 92] = [x] + 92 = 15 + 92 = 107$.

If $y = 3[x] + 1 = 4[x - 1] - 10$,then $[x + 2y]$ is equal to (where $[.]$ is the $Greatest$ $Integer$ $Function$)

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