What is 5-sqrt(20x+4)>=-3 ?

The solution to 5-sqrt(20x+4)>=-3 is -1/5 <= x<= 3

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5-sqrt(20x+4)>=-3

5 - 20 x + 4 \geq - 3

- \frac{1}{5} \leq x \leq 3

Interval Notation

[- \frac{1}{5}, 3]

Decimal Notation

- 0.2 \leq x \leq 3

Solution steps

5 - 20 x + 4 \geq - 3

Move

5

to the right side

- 20 x + 4 \geq - 8

Multiply both sides by

- 1

20 x + 4 \leq 8

Square both sides

(20 x + 4)^{2} \leq 8^{2}

Simplify

20 x + 4 \leq 64

20 x + 4 \leq 64 : x \leq 3

x \leq 3

Find singularity points

Find non-negative values for radicals:

x \geq - \frac{1}{5}

Combine the intervals

x \leq 3 and x \geq - \frac{1}{5}

Merge Overlapping Intervals

- \frac{1}{5} \leq x \leq 3

\frac{( x + 5 ) ( x + 3 )}{x - 1} \leq 0

t^{2} = 0

\frac{1}{3} - \frac{2}{5}

\frac{1}{3} + \frac{5}{9}

3 y - 10 \leq 8