What is 4/3 x+8>= 3(1-1/(3x)) ?

The solution to 4/3 x+8>= 3(1-1/(3x)) is (-15-sqrt(177))/8 0

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4/3 x+8>= 3(1-1/(3x))

\frac{4}{3} x + 8 \geq 3 (1 - \frac{1}{3 x})

\frac{- 15 - 177}{8} \leq x \leq \frac{177 - 15}{8} or x > 0

Interval Notation

[\frac{- 15 - 177}{8}, \frac{177 - 15}{8}] \cup (0, \infty)

Decimal Notation

- 3.53801 \dots \leq x \leq - 0.21198 \dots or x > 0

Solution steps

\frac{4}{3} x + 8 \geq 3 (1 - \frac{1}{3 x})

Rewrite in standard form

\frac{4 x ^{2} + 3 + 15 x}{x} \geq 0

Factor

4 x^{2} + 3 + 15 x : (x - \frac{- 15 + 177}{8}) (x - \frac{- 15 - 177}{8})

\frac{( x - \frac{- 15 + 177}{8} ) ( x - \frac{- 15 - 177}{8} )}{x} \geq 0

Identify the intervals

\frac{- 15 - 177}{8} \leq x \leq \frac{177 - 15}{8} or x > 0

g^{\frac{4}{7}} \cdot g^{\frac{3}{7}}

\frac{5}{6} x - 2 = \frac{7}{8}

2 x^{2} - 11 x - 2 = 0

2 k^{2} + 22 k = 74

x + 11 = \frac{( x - 13 ) ^{2}}{2}

What is 4/3 x+8>= 3(1-1/(3x)) ?
The solution to 4/3 x+8>= 3(1-1/(3x)) is (-15-sqrt(177))/8 <= x<= (sqrt(177)-15)/8 \lor x>0