For how many integer values of n will the value of the expression 4n + 7 be an integer greater than ...

For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

Answer/Solution

Steps/Work

From first constraint
4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 200
4n< 193
n < 48. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 48)
Combining the two
-1.5 < n<48.25
n = 1 to 48 (48 integers)
and n = -1 and 0
so 50 integers.
C is the answer

General Calculator / Auto Solver

For how many integer values of n will the value of the expression n + be an integer greater than and less than ?

Calculated Answer

Step by Step Solution

In order to solve problem, you must evaluate floor((n₃ - n₁) / n₀) - floor((n₂ - n₁) / n₀).

n₀ =	4
n₁ =	7
n₂ =	1
n₃ =	200

floor((n₃ - n₁) / n₀) - floor((n₂ - n₁) / n₀)
Evaluate n₃ - n₁ = 193
floor(193 / n₀) - floor((n₂ - n₁) / n₀)
Evaluate 193 / n₀ = 48.25
floor(48.25) - floor((n₂ - n₁) / n₀)
Evaluate floor(48.25) = 48
48 - floor((n₂ - n₁) / n₀)
Evaluate n₂ - n₁ = -6
48 - floor(-6 / n₀)
Evaluate -6 / n₀ = -1.5
48 - floor(-1.5)
Evaluate floor(-1.5) = -2
48 - -2
Evaluate 48 - -2 = 50
50
The answer to the problem and the result of floor((n₃ - n₁) / n₀) - floor((n₂ - n₁) / n₀) is 50

Quiz

Answer/Solution

Steps/Work

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Calculated Answer

Step by Step Solution