What is sqrt(5x-4)+sqrt(3x+1)<3 ?

The solution to sqrt(5x-4)+sqrt(3x+1)<3 is 4/5 <= x<1

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sqrt(5x-4)+sqrt(3x+1)<3

5 x - 4 + 3 x + 1 < 3

\frac{4}{5} \leq x < 1

Interval Notation

[\frac{4}{5}, 1)

Decimal Notation

0.8 \leq x < 1

Solution steps

5 x - 4 + 3 x + 1 < 3

Subtract

3 x + 1

from both sides

5 x - 4 + 3 x + 1 - 3 x + 1 < 3 - 3 x + 1

Simplify

5 x - 4 < 3 - 3 x + 1

f (x) < g (x)

then

g (x) > 0

3 - 3 x + 1 > 0 : x < \frac{8}{3}

5 x - 4 < 3 - 3 x + 1 : x < 1

Find singularity points

Find non-negative values for radicals:

x \geq \frac{4}{5}

Combine the intervals

x < \frac{8}{3} and x < 1 and x \geq \frac{4}{5}

Merge Overlapping Intervals

\frac{4}{5} \leq x < 1

Verify Solutions:

\frac{4}{5} \leq x < 1

True

The solution is

\frac{4}{5} \leq x < 1

2 x - 1 < x

x - 1 < x^{2} + 1

2 + x - x^{2} < x + 2

2 x + 14 > x + 3

\frac{( x - 3 )}{( x - 2 )} > 1

What is sqrt(5x-4)+sqrt(3x+1)<3 ?
The solution to sqrt(5x-4)+sqrt(3x+1)<3 is 4/5 <= x<1