What is 0.4<|x-7/5 |<= 5/3 ?

The solution to 0.4<|x-7/5 |<= 5/3 is -4/15 <= x<1\lor 1.8<x<= 46/15

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0.4<|x-7/5 |<= 5/3

0.4 < x - \frac{7}{5} \leq \frac{5}{3}

- \frac{4}{15} \leq x < 1 or 1.8 < x \leq \frac{46}{15}

Interval Notation

[- \frac{4}{15}, 1) \cup (1.8, \frac{46}{15}]

Decimal Notation

- 0.26666 \dots \leq x < 1 or 1.8 < x \leq 3.06666 \dots

Solution steps

0.4 < x - \frac{7}{5} \leq \frac{5}{3}

a < u \leq b

then

a < u and u \leq b

0.4 < x - \frac{7}{5} and x - \frac{7}{5} \leq \frac{5}{3}

0.4 < x - \frac{7}{5} : x < 1 or x > 1.8

x - \frac{7}{5} \leq \frac{5}{3} : - \frac{4}{15} \leq x \leq \frac{46}{15}

Combine the intervals

(x < 1 or x > 1.8) and - \frac{4}{15} \leq x \leq \frac{46}{15}

Merge Overlapping Intervals

- \frac{4}{15} \leq x < 1 or 1.8 < x \leq \frac{46}{15}

- 8 > y > 12

\frac{- ( 5 )}{3} \leq x < e

8.1 < y < 8.2

- 3 < x - 1 \leq 5

2 x - 3 < x + 1 < 4 x + 7

What is 0.4<|x-7/5 |<= 5/3 ?
The solution to 0.4<|x-7/5 |<= 5/3 is -4/15 <= x<1\lor 1.8<x<= 46/15