What is -4|3x-1|>-16 ?

The solution to -4|3x-1|>-16 is -1<x< 5/3

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-4|3x-1|>-16

- 4 ∣ 3 x - 1 ∣ > - 16

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

Interval Notation

(- 1, \frac{5}{3})

Decimal Notation

- 1 < x < 1.66666 \dots

Solution steps

- 4 ∣ 3 x - 1 ∣ > - 16

Multiply both sides by

- 1

4 ∣ 3 x - 1 ∣ < 16

Divide both sides by

4

∣ 3 x - 1 ∣ < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < 3 x - 1 < 4

3 x - 1 > - 4 and 3 x - 1 < 4

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

Merge Overlapping Intervals

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

2 x^{2} - 6 x + 2 = 0

(3 - 4 x) (3 x - 7) \geq 0

x^{2} (2 x)

(3 - 3)^{2}

2 \cdot 4^{\frac{3}{2}}