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

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

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

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

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

Solution steps

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

Rewrite in standard form

\frac{- 2 x ^{2} - 3 x + 2}{x + 1} \geq 0

Factor

\frac{- 2 x ^{2} - 3 x + 2}{x + 1} : \frac{- ( 2 x - 1 ) ( x + 2 )}{x + 1}

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

c^{4} - 1

(\frac{16}{3})^{2}

3 x^{2} - 12 x + 4 = 0

(\frac{29}{41})^{5}

\frac{3}{2 + 1}

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