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

The solution to |((3-4x))/5 |<= 4 is -17/4 <= x<= 23/4

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

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

- \frac{17}{4} \leq x \leq \frac{23}{4}

Solution steps

\frac{3 - 4 x}{5} \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq \frac{3 - 4 x}{5} \leq 4

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

x \leq \frac{23}{4} and x \geq - \frac{17}{4}

Merge Overlapping Intervals

- \frac{17}{4} \leq x \leq \frac{23}{4}

34 + 21 x - x^{2} \leq - 1

∣ x + 2 ∣ + ∣ x ∣ + ∣ x - 2 ∣ > 6

\frac{( x - 3 )}{( x + 1 )} \leq 2

x^{2} + 3 x + x^{2} - 2 \geq 0

∣ x - 2 ∣ < \frac{1}{6}

What is |((3-4x))/5 |<= 4 ?
The solution to |((3-4x))/5 |<= 4 is -17/4 <= x<= 23/4