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

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

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

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

x \leq - \frac{1}{2} or \frac{1}{2} < x \leq \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{2}] \cup (\frac{1}{2}, \frac{1}{2}]

Decimal Notation

x \leq - 0.70710 \dots or 0.5 < x \leq 0.70710 \dots

Solution steps

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

Rewrite in standard form

\frac{2 x ^{2} - 1}{2 x - 1} \leq 0

Factor

\frac{2 x ^{2} - 1}{2 x - 1} : \frac{( 2 x + 1 ) ( 2 x - 1 )}{2 x - 1}

\frac{( 2 x + 1 ) ( 2 x - 1 )}{2 x - 1} \leq 0

Identify the intervals

x \leq - \frac{1}{2} or \frac{1}{2} < x \leq \frac{1}{2}

\frac{2 a ^{\frac{3}{2}} b}{8 a ^{\frac{7}{2}} b ^{\frac{1}{2}}}

4^{(- \frac{3}{8})} + 5 = 3^{\frac{3}{8}} + 4

1 \frac{2}{3} x + (2 x + 1) (13 x - 1) \geq 0

6^{2}

2 (x + 10) = x + 24

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