What is |(6x+3)/(4x-2)|<12 ?

The solution to |(6x+3)/(4x-2)| 9/14

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|(6x+3)/(4x-2)|<12

\frac{6 x + 3}{4 x - 2} < 12

x < \frac{7}{18} or x > \frac{9}{14}

Interval Notation

(- \infty, \frac{7}{18}) \cup (\frac{9}{14}, \infty)

Decimal Notation

x < 0.38888 \dots or x > 0.64285 \dots

Solution steps

\frac{6 x + 3}{4 x - 2} < 12

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 12 < \frac{6 x + 3}{4 x - 2} < 12

\frac{6 x + 3}{4 x - 2} > - 12 and \frac{6 x + 3}{4 x - 2} < 12

(x < \frac{7}{18} or x > \frac{1}{2}) and (x < \frac{1}{2} or x > \frac{9}{14})

Merge Overlapping Intervals

x < \frac{7}{18} or x > \frac{9}{14}

\frac{9}{25}

\frac{k}{2} + \frac{1}{2} = 3

4 - (5 - x) = 2 x

z^{2} = 144

y + 15 = - 15

What is |(6x+3)/(4x-2)|<12 ?
The solution to |(6x+3)/(4x-2)|<12 is x< 7/18 \lor x> 9/14