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

The solution to 1<= ((2-x))/((x+1))<= 2 is 0<= x<= 1/2

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

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

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

Interval Notation

[0, \frac{1}{2}]

Decimal Notation

0 \leq x \leq 0.5

Solution steps

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

a \leq u \leq b

then

a \leq u and u \leq b

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

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

\frac{2 - x}{x + 1} \leq 2 : x < - 1 or x \geq 0

Combine the intervals

- 1 < x \leq \frac{1}{2} and (x < - 1 or x \geq 0)

Merge Overlapping Intervals

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

0 < - \frac{x}{3} < 1

3 x + 1 > 2 x + 6 > x + 5

- 3 < 2 x + 3 < 5

3 < x < 10

- 2 + x < 3 x < 4 + x

What is 1<= ((2-x))/((x+1))<= 2 ?
The solution to 1<= ((2-x))/((x+1))<= 2 is 0<= x<= 1/2