What is 1/(2-x)>= x+2 ?

The solution to 1/(2-x)>= x+2 is x<=-sqrt(3)\lor sqrt(3)<= x<2

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1/(2-x)>= x+2

\frac{1}{2 - x} \geq x + 2

x \leq - 3 or 3 \leq x < 2

Interval Notation

(- \infty, - 3] \cup [3, 2)

Decimal Notation

x \leq - 1.73205 \dots or 1.73205 \dots \leq x < 2

Solution steps

\frac{1}{2 - x} \geq x + 2

Rewrite in standard form

\frac{x ^{2} - 3}{2 - x} \geq 0

Factor

\frac{x ^{2} - 3}{2 - x} : \frac{( x + 3 ) ( x - 3 )}{2 - x}

\frac{( x + 3 ) ( x - 3 )}{2 - x} \geq 0

Identify the intervals

x \leq - 3 or 3 \leq x < 2

9 x^{3} - 36 x^{2} - 25 x + 100

5 x^{2} + 30 x = 125

\frac{k}{2} - 4 = 18

3 y + 6 (3) = 27

\frac{1}{2 ^{4}}

What is 1/(2-x)>= x+2 ?
The solution to 1/(2-x)>= x+2 is x<=-sqrt(3)\lor sqrt(3)<= x<2