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

The solution to sqrt(4-3x)<= 1-5x is x<= (-sqrt(349)+7)/(50)

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

4 - 3 x \leq 1 - 5 x

x \leq \frac{- 349 + 7}{50}

Interval Notation

(- \infty, \frac{- 349 + 7}{50}]

Decimal Notation

x \leq - 0.23363 \dots

Solution steps

4 - 3 x \leq 1 - 5 x

f (x) \leq g (x)

then

g (x) \geq 0

1 - 5 x \geq 0 : x \leq \frac{1}{5}

4 - 3 x \leq 1 - 5 x : x \leq \frac{- 349 + 7}{50} or x \geq \frac{349 + 7}{50}

Find singularity points

Find non-negative values for radicals:

x \leq \frac{4}{3}

Combine the intervals

x \leq \frac{1}{5} and (x \leq \frac{- 349 + 7}{50} or x \geq \frac{349 + 7}{50}) and x \leq \frac{4}{3}

Merge Overlapping Intervals

x \leq \frac{- 349 + 7}{50}

Verify Solutions:

x \leq \frac{- 349 + 7}{50}

True

The solution is

x \leq \frac{- 349 + 7}{50}

\frac{3}{4} c - \frac{1}{4} c + 3 = 7

- \frac{5}{2} (- 2)

3 a^{2} - 12 a + 8 = 71

\frac{4}{3} + \frac{1}{3}

4 + \frac{2}{3}

What is sqrt(4-3x)<= 1-5x ?
The solution to sqrt(4-3x)<= 1-5x is x<= (-sqrt(349)+7)/(50)