What is |(3x-4)/5 |< 1/4 ?

The solution to |(3x-4)/5 |< 1/4 is 11/12 <x< 7/4

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|(3x-4)/5 |< 1/4

\frac{3 x - 4}{5} < \frac{1}{4}

\frac{11}{12} < x < \frac{7}{4}

Interval Notation

(\frac{11}{12}, \frac{7}{4})

Decimal Notation

0.91666 \dots < x < 1.75

Solution steps

\frac{3 x - 4}{5} < \frac{1}{4}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{1}{4} < \frac{3 x - 4}{5} < \frac{1}{4}

\frac{3 x - 4}{5} > - \frac{1}{4} and \frac{3 x - 4}{5} < \frac{1}{4}

x > \frac{11}{12} and x < \frac{7}{4}

Merge Overlapping Intervals

\frac{11}{12} < x < \frac{7}{4}

7 x + 6 \leq 2 x^{2}

54 = 54 - 9 t

x + 8 > 12

55 \cdot 515

- 4 x + 1 \leq - 3