What is (-1)/5 <= 3 x/(10)+1< 2/5 ?

The solution to (-1)/5 <= 3 x/(10)+1< 2/5 is -4<= x<-2

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(-1)/5 <= 3 x/(10)+1< 2/5

\frac{- 1}{5} \leq 3 \frac{x}{10} + 1 < \frac{2}{5}

- 4 \leq x < - 2

Interval Notation

[- 4, - 2)

Solution steps

\frac{- 1}{5} \leq 3 \cdot \frac{x}{10} + 1 < \frac{2}{5}

a \leq u < b

then

a \leq u and u < b

\frac{- 1}{5} \leq 3 \cdot \frac{x}{10} + 1 and 3 \cdot \frac{x}{10} + 1 < \frac{2}{5}

\frac{- 1}{5} \leq 3 \cdot \frac{x}{10} + 1 : x \geq - 4

3 \cdot \frac{x}{10} + 1 < \frac{2}{5} : x < - 2

Combine the intervals

x \geq - 4 and x < - 2

Merge Overlapping Intervals

- 4 \leq x < - 2

0 < \frac{6}{x} < \frac{8}{9}

3 < 2 x + 1 < 5

- 4 < 2 x - 3 < 4

9 < 7 x - 5 < 16

2 x < x - 4 < x + 8

What is (-1)/5 <= 3 x/(10)+1< 2/5 ?
The solution to (-1)/5 <= 3 x/(10)+1< 2/5 is -4<= x<-2