What is | 3/4 x+1/5 |<= 1/20 ?

The solution to | 3/4 x+1/5 |<= 1/20 is -1/3 <= x<=-1/5

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| 3/4 x+1/5 |<= 1/20

\frac{3}{4} x + \frac{1}{5} \leq \frac{1}{20}

- \frac{1}{3} \leq x \leq - \frac{1}{5}

Solution steps

\frac{3}{4} x + \frac{1}{5} \leq \frac{1}{20}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{20} \leq \frac{3}{4} x + \frac{1}{5} \leq \frac{1}{20}

\frac{3}{4} x + \frac{1}{5} \geq - \frac{1}{20} and \frac{3}{4} x + \frac{1}{5} \leq \frac{1}{20}

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

Merge Overlapping Intervals

- \frac{1}{3} \leq x \leq - \frac{1}{5}

- 5 x < 35

x^{3} + 2 x^{2} - 6 x - 2 = x^{3} + x^{2} - 7 x + 18

\frac{3 x}{5} = \frac{4 x}{3} - 22

p^{2} - 144 = 0

- 5 - \frac{1}{2}

What is | 3/4 x+1/5 |<= 1/20 ?
The solution to | 3/4 x+1/5 |<= 1/20 is -1/3 <= x<=-1/5