What is -3sqrt(11r+3)>=-15 ?

The solution to -3sqrt(11r+3)>=-15 is -3/11 <= r<= 2

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-3sqrt(11r+3)>=-15

- 3 11 r + 3 \geq - 15

- \frac{3}{11} \leq r \leq 2

Interval Notation

[- \frac{3}{11}, 2]

Decimal Notation

- 0.27272 \dots \leq r \leq 2

Solution steps

- 3 11 r + 3 \geq - 15

Multiply both sides by

- 1

(reverse the inequality)

(- 3 11 r + 3) (- 1) \leq (- 15) (- 1)

Simplify

3 11 r + 3 \leq 15

Divide both sides by

3

\frac{3 11 r + 3}{3} \leq \frac{15}{3}

Simplify

11 r + 3 \leq 5

Square both sides

(11 r + 3)^{2} \leq 5^{2}

Simplify

11 r + 3 \leq 25

11 r + 3 \leq 25 : r \leq 2

r \leq 2

Find singularity points

Find non-negative values for radicals:

r \geq - \frac{3}{11}

Combine the intervals

r \leq 2 and r \geq - \frac{3}{11}

Merge Overlapping Intervals

- \frac{3}{11} \leq r \leq 2

\frac{7}{3} (\frac{1}{2} v - \frac{10}{3}) = - \frac{35}{3} - \frac{1}{2} v

5 (x - 2)^{2} + 6 = 86

6 a^{2} - 11 a + 4

x^{2} + 7 x + 11 = 0

3^{x} \cdot 2^{x}

What is -3sqrt(11r+3)>=-15 ?
The solution to -3sqrt(11r+3)>=-15 is -3/11 <= r<= 2