What is |(3-4x)-7|< 1/4 ?

The solution to |(3-4x)-7|< 1/4 is -17/16 <x<-15/16

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|(3-4x)-7|< 1/4

∣ (3 - 4 x) - 7 ∣ < \frac{1}{4}

- \frac{17}{16} < x < - \frac{15}{16}

Interval Notation

(- \frac{17}{16}, - \frac{15}{16})

Decimal Notation

- 1.0625 < x < - 0.9375

Solution steps

∣ 3 - 4 x - 7 ∣ < \frac{1}{4}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{1}{4} < 3 - 4 x - 7 < \frac{1}{4}

3 - 4 x - 7 > - \frac{1}{4} and 3 - 4 x - 7 < \frac{1}{4}

x < - \frac{15}{16} and x > - \frac{17}{16}

Merge Overlapping Intervals

- \frac{17}{16} < x < - \frac{15}{16}

3 x + 2 (4 x + 2) \leq 2 (6 x + 1)

9 x^{2} + 18 x + 4 = 0

x^{2} + 49 x = 0

2^{3} - [4 (5 - 3)^{3}] = - 8 x

15 x^{2} + 4 x - 4 = 0