What is -2+sqrt(3m-1)<4 ?

The solution to -2+sqrt(3m-1)<4 is 1/3 <= m< 37/3

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-2+sqrt(3m-1)<4

- 2 + 3 m - 1 < 4

\frac{1}{3} \leq m < \frac{37}{3}

Interval Notation

[\frac{1}{3}, \frac{37}{3})

Decimal Notation

0.33333 \dots \leq m < 12.33333 \dots

Solution steps

- 2 + 3 m - 1 < 4

Move

2

to the right side

3 m - 1 < 6

Square both sides

(3 m - 1)^{2} < 6^{2}

Simplify

3 m - 1 < 36

3 m - 1 < 36 : m < \frac{37}{3}

m < \frac{37}{3}

Find singularity points

Find non-negative values for radicals:

m \geq \frac{1}{3}

Combine the intervals

m < \frac{37}{3} and m \geq \frac{1}{3}

Merge Overlapping Intervals

\frac{1}{3} \leq m < \frac{37}{3}

\frac{b ^{4}}{b ^{2}} c

- 15 x^{2} + 780 x - 1048 = 0

\frac{1}{6} (x - 15) > x + 20

2 x - 3 = x + 1

16 k^{2} - 40 k + 25