What is 1/(2x-2)<= 3/(2x+2) ?

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1/(2x-2)<= 3/(2x+2)

\frac{1}{2 x - 2} \leq \frac{3}{2 x + 2}

- 1 < x < 1 or x \geq 2

Interval Notation

(- 1, 1) \cup [2, \infty)

Solution steps

\frac{1}{2 x - 2} \leq \frac{3}{2 x + 2}

Rewrite in standard form

\frac{- 2 x + 4}{( x - 1 ) ( x + 1 )} \leq 0

Factor

\frac{- 2 x + 4}{( x - 1 ) ( x + 1 )} : \frac{- 2 ( x - 2 )}{( x - 1 ) ( x + 1 )}

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

- 1 < x < 1 or x \geq 2

36 x^{2} - 16

\frac{5}{64}

4 \leq ∣ x + 2 ∣

- 81 + 9 a^{10}

x^{2} + 17 x + 52

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