What is | 2/3 x+1/5 |<= 1/15 ?

The solution to | 2/3 x+1/5 |<= 1/15 is -2/5 <= x<=-1/5

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| 2/3 x+1/5 |<= 1/15

\frac{2}{3} x + \frac{1}{5} \leq \frac{1}{15}

- \frac{2}{5} \leq x \leq - \frac{1}{5}

Interval Notation

[- \frac{2}{5}, - \frac{1}{5}]

Decimal Notation

- 0.4 \leq x \leq - 0.2

Solution steps

\frac{2}{3} x + \frac{1}{5} \leq \frac{1}{15}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{15} \leq \frac{2}{3} x + \frac{1}{5} \leq \frac{1}{15}

\frac{2}{3} x + \frac{1}{5} \geq - \frac{1}{15} and \frac{2}{3} x + \frac{1}{5} \leq \frac{1}{15}

x \geq - \frac{2}{5} and x \leq - \frac{1}{5}

Merge Overlapping Intervals

- \frac{2}{5} \leq x \leq - \frac{1}{5}

48 + 3

- 3 ∣ 2 x - 16 ∣ + 25 < 4

50 > \frac{m}{- 3}

x^{3} < 121 x

What is | 2/3 x+1/5 |<= 1/15 ?
The solution to | 2/3 x+1/5 |<= 1/15 is -2/5 <= x<=-1/5