What is 6-sqrt(2y+1)<3 ?

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6-sqrt(2y+1)<3

6 - 2 y + 1 < 3

y > 4

Interval Notation

(4, \infty)

Solution steps

6 - 2 y + 1 < 3

Move

6

to the right side

- 2 y + 1 < - 3

Multiply both sides by

- 1

2 y + 1 > 3

Square both sides

(2 y + 1)^{2} > 3^{2}

Simplify

2 y + 1 > 9

2 y + 1 > 9 : y > 4

y > 4

Find singularity points

Find non-negative values for radicals:

y \geq - \frac{1}{2}

Combine the intervals

y > 4 and y \geq - \frac{1}{2}

Merge Overlapping Intervals

y > 4

f (x) = (\frac{1}{2})^{x + 3}

\frac{1}{4} \times \frac{1}{4}

6 x^{2} + 5 x y - 4 y^{2}

2 x^{2} - 1