What is |(3x-2)-7|< 1/2 ?

The solution to |(3x-2)-7|< 1/2 is 17/6 <x< 19/6

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|(3x-2)-7|< 1/2

∣ (3 x - 2) - 7 ∣ < \frac{1}{2}

\frac{17}{6} < x < \frac{19}{6}

Solution steps

∣ 3 x - 2 - 7 ∣ < \frac{1}{2}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{1}{2} < 3 x - 2 - 7 < \frac{1}{2}

3 x - 2 - 7 > - \frac{1}{2} and 3 x - 2 - 7 < \frac{1}{2}

x > \frac{17}{6} and x < \frac{19}{6}

Merge Overlapping Intervals

\frac{17}{6} < x < \frac{19}{6}

\frac{3 x - 4}{2 x + 4} \leq 1

3 x \geq 8

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(\frac{y}{3})^{- 7}

24 x y + 25 y^{2} - 20 x - 30 y^{3}