What is |((3x-4))/2 |< 5/12 ?

The solution to |((3x-4))/2 |< 5/12 is 19/18 <x< 29/18

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|((3x-4))/2 |< 5/12

\frac{( 3 x - 4 )}{2} < \frac{5}{12}

\frac{19}{18} < x < \frac{29}{18}

Solution steps

\frac{3 x - 4}{2} < \frac{5}{12}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{5}{12} < \frac{3 x - 4}{2} < \frac{5}{12}

\frac{3 x - 4}{2} > - \frac{5}{12} and \frac{3 x - 4}{2} < \frac{5}{12}

x > \frac{19}{18} and x < \frac{29}{18}

Merge Overlapping Intervals

\frac{19}{18} < x < \frac{29}{18}

\frac{( x + 1 )}{( x - 3 )} < \frac{1}{3}

∣ x + 1 ∣ + ∣ x + 2 ∣ \leq 10

\frac{3 ∣ x ∣ - 2}{∣ x ∣ - 1} \geq 2

x ∣ x + 1 ∣ + ∣ x ∣ > 3

∣ 3 - 5 x ∣ \leq 10

What is |((3x-4))/2 |< 5/12 ?
The solution to |((3x-4))/2 |< 5/12 is 19/18 <x< 29/18