Question

If 2[x] + 1 = 3[x + 1] – 8, where [·] represents the greatest integer function, then value of [x + 4] equals

Answer 1

it has given that , 2[x] + 1 = 3[x + 1] - 8 where [.] represents the greatest integer function.

we have to find the value of [x + 4]

solution : we know, [x + k] = [x] + k, for any integer k.

so, [x + 1] = [x] + 1

now, 2[x] + 1 = 3([x] + 1) - 8

⇒2[x] + 1 = 3[x] + 3 - 8

⇒1 + 5 = [x]

⇒6 = [x]

so, 6 ≤ x < 7

now [x + 4] = [x] + 4 = 6 + 4 = 10

Therefore the value of [x + 4] = 10

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Answer 2

GivEn :-

2 [x] +1 = 3 [x+1]-8

Where [-] Represent the Greatest Integer Function

To FinD :-

• The Value of [x+4]

SoluTioN :-

We know that,

• [x+k] = [x]+k, for any Integer k

By this,

• [x+1] = [x]+1

Now :-

• 2[x] +1 = 3[x]+1 -8

• 2[x] +1 = 3[x]+3-8

• 2[x]+1 = 3[x] +3-8

• 1 + 5 = [x]

• [x] = 6

Since, [x] = 6 ≤ x < 7

Now, [x+4] = [x] + 4 = 6+4 = 10

$\boxed{ \bold{ \red{★Hence \: the \: value \: of \: [x + 4] = 10}{} }{} }{}$