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Popular >

3.5n-1356-1.28*sqrt(2.916n)>0

Solution

3.5 n - 1356 - 1.28 \cdot 2.916 n > 0

n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}

Interval Notation

(\frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}, \infty)

Decimal Notation

n > 399.91737 \dots

Solution steps

3.5 n - 1356 - 1.28 2.916 n > 0

Subtract

3.5 n - 1356

from both sides

3.5 n - 1356 - 1.28 2.916 n - (3.5 n - 1356) > 0 - (3.5 n - 1356)

Simplify

- 1.28 2.916 n > - (3.5 n - 1356)

Multiply both sides by

- 1

(reverse the inequality)

(- 1.28 2.916 n) (- 1) < (- (3.5 n - 1356)) (- 1)

Simplify

1.28 2.916 n < 3.5 n - 1356

Multiply both sides by

100

128 2.916 n < 350 n - 135600

Divide both sides by

128

2.916 n < \frac{25 ( 7 n - 2712 )}{64}

f (x) < g (x)

then

g (x) > 0

\frac{25 ( 7 n - 2712 )}{64} > 0 : n > \frac{2712}{7}

2.916 n < \frac{25 ( 7 n - 2712 )}{64} : n < \frac{- 2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000} or n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}

Find singularity points

Find non-negative values for radicals:

n \geq 0

Combine the intervals

n > \frac{2712}{7} and (n < \frac{- 2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000} or n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}) and n \geq 0

Merge Overlapping Intervals

n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}

Verify Solutions:

n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}

True

The solution is

n > \frac{2374194393 6 ^{2} - 5.63113 E 20 + 23741943936}{61250000}

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