What is |(4x-1)-11|< 1/4 ?

The solution to |(4x-1)-11|< 1/4 is 47/16 <x< 49/16

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|(4x-1)-11|< 1/4

∣ (4 x - 1) - 11 ∣ < \frac{1}{4}

\frac{47}{16} < x < \frac{49}{16}

Interval Notation

(\frac{47}{16}, \frac{49}{16})

Decimal Notation

2.9375 < x < 3.0625

Solution steps

∣ 4 x - 1 - 11 ∣ < \frac{1}{4}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{1}{4} < 4 x - 1 - 11 < \frac{1}{4}

4 x - 1 - 11 > - \frac{1}{4} and 4 x - 1 - 11 < \frac{1}{4}

x > \frac{47}{16} and x < \frac{49}{16}

Merge Overlapping Intervals

\frac{47}{16} < x < \frac{49}{16}

1 - 2 ln (x) < 3

\frac{( x ^{6} )}{x ^{5}}

∣ 2 x - 7 ∣ - 2 > 3

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1350 = \frac{x ^{2}}{2} + 55.8 x - x^{2}