What is | 5/6 x+1/5 |<= 1/30 ?

The solution to | 5/6 x+1/5 |<= 1/30 is -7/25 <= x<=-1/5

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| 5/6 x+1/5 |<= 1/30

\frac{5}{6} x + \frac{1}{5} \leq \frac{1}{30}

- \frac{7}{25} \leq x \leq - \frac{1}{5}

Interval Notation

[- \frac{7}{25}, - \frac{1}{5}]

Decimal Notation

- 0.28 \leq x \leq - 0.2

Solution steps

\frac{5}{6} x + \frac{1}{5} \leq \frac{1}{30}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{30} \leq \frac{5}{6} x + \frac{1}{5} \leq \frac{1}{30}

\frac{5}{6} x + \frac{1}{5} \geq - \frac{1}{30} and \frac{5}{6} x + \frac{1}{5} \leq \frac{1}{30}

x \geq - \frac{7}{25} and x \leq - \frac{1}{5}

Merge Overlapping Intervals

- \frac{7}{25} \leq x \leq - \frac{1}{5}

x (x - 2) = - x^{2}

(5 x^{4} y^{3})^{3}

∣ 5 x ∣ > - 4

\frac{2 x - 3}{x + 5} \geq 2

5 x^{2} - 7 x + 2

What is | 5/6 x+1/5 |<= 1/30 ?
The solution to | 5/6 x+1/5 |<= 1/30 is -7/25 <= x<=-1/5