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Popular >

-1<((2x))/((x-1))<= 4

Solution

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

Solution

x < \frac{1}{3} or x \geq 2

+2

Interval Notation

(- \infty, \frac{1}{3}) \cup [2, \infty)

Decimal Notation

x < 0.33333 \dots or x \geq 2

Solution steps

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

If

a < u \leq b

then

a < u and u \leq b

- 1 < \frac{( 2 x )}{( x - 1 )} and \frac{( 2 x )}{( x - 1 )} \leq 4

- 1 < \frac{2 x}{x - 1} : x < \frac{1}{3} or x > 1

\frac{2 x}{x - 1} \leq 4 : x < 1 or x \geq 2

Combine the intervals

(x < \frac{1}{3} or x > 1) and (x < 1 or x \geq 2)

Merge Overlapping Intervals

x < \frac{1}{3} or x \geq 2

Popular Examples

- 3 < 2 x - 1 < 19

- 7 < 4 r + 1 < 13

1/6 > x/(15)>(-2)/5

\frac{1}{6} > \frac{x}{15} > \frac{- 2}{5}

- 4 < x < \frac{36}{7}

1 < 5 - 3 x < 2

Frequently Asked Questions (FAQ)

What is -1<((2x))/((x-1))<= 4 ?
The solution to -1<((2x))/((x-1))<= 4 is x< 1/3 \lor x>= 2