What is 4sqrt(2x-3)<12 ?

The solution to 4sqrt(2x-3)<12 is 3/2 <= x<6

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4sqrt(2x-3)<12

4 2 x - 3 < 12

\frac{3}{2} \leq x < 6

Interval Notation

[\frac{3}{2}, 6)

Decimal Notation

1.5 \leq x < 6

Solution steps

4 2 x - 3 < 12

Divide both sides by

4

\frac{4 2 x - 3}{4} < \frac{12}{4}

Simplify

2 x - 3 < 3

Square both sides

(2 x - 3)^{2} < 3^{2}

Simplify

2 x - 3 < 9

2 x - 3 < 9 : x < 6

x < 6

Find singularity points

Find non-negative values for radicals:

x \geq \frac{3}{2}

Combine the intervals

x < 6 and x \geq \frac{3}{2}

Merge Overlapping Intervals

\frac{3}{2} \leq x < 6

\frac{1}{9} \cdot \frac{5}{4}

\frac{- 6 \cdot 1 0 ^{- 9}}{8.85 \cdot 1 0 ^{- 12}}

- 34

ln (ln (1))

3 k^{2} - 25 k - 18