What is sqrt(6x-5)-x<0 ?

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sqrt(6x-5)-x<0

6 x - 5 - x < 0

\frac{5}{6} \leq x < 1 or x > 5

Interval Notation

[\frac{5}{6}, 1) \cup (5, \infty)

Decimal Notation

0.83333 \dots \leq x < 1 or x > 5

Solution steps

6 x - 5 - x < 0

Add

x

to both sides

6 x - 5 - x + x < 0 + x

Simplify

6 x - 5 < x

f (x) < g (x)

then

g (x) > 0

x > 0

6 x - 5 < x : x < 1 or x > 5

Find singularity points

Find non-negative values for radicals:

x \geq \frac{5}{6}

Combine the intervals

x > 0 and (x < 1 or x > 5) and x \geq \frac{5}{6}

Merge Overlapping Intervals

\frac{5}{6} \leq x < 1 or x > 5

Verify Solutions:

\frac{5}{6} \leq x < 1

True

, x > 5

True

The solution is

\frac{5}{6} \leq x < 1 or x > 5

(x - 0.2)^{2} (x - 0.4)^{2}

\frac{\frac{y}{x} - \frac{x}{y}}{\frac{1}{y} - \frac{1}{x}}

x + 4 = 2 x + 1

4 (x + 2 y + z)^{2} - 9 (x - 2 y + z)^{2}

\frac{2 ^{9}}{2 ^{5}}