What is |(3-(5x-2))/4 |<= 8 ?

The solution to |(3-(5x-2))/4 |<= 8 is -27/5 <= x<= 37/5

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|(3-(5x-2))/4 |<= 8

\frac{3 - ( 5 x - 2 )}{4} \leq 8

- \frac{27}{5} \leq x \leq \frac{37}{5}

Solution steps

\frac{3 - ( 5 x - 2 )}{4} \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq \frac{3 - ( 5 x - 2 )}{4} \leq 8

\frac{3 - ( 5 x - 2 )}{4} \geq - 8 and \frac{3 - ( 5 x - 2 )}{4} \leq 8

x \leq \frac{37}{5} and x \geq - \frac{27}{5}

Merge Overlapping Intervals

- \frac{27}{5} \leq x \leq \frac{37}{5}

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

x^{3} - 1 \geq 1 - x

∣ x ∣ < 2

x^{2} - 2 x + 3 < - 3

\frac{1}{x - 2} < 4

What is |(3-(5x-2))/4 |<= 8 ?
The solution to |(3-(5x-2))/4 |<= 8 is -27/5 <= x<= 37/5