What is 3|x|e^{|x|}<16 ?

The solution to 3|x|e^{|x|}<16 is -\W_{0}(16/3)<x<\W_{0}(16/3)

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3|x|e^{|x|}<16

3 ∣ x ∣ e^{∣ x ∣} < 16

- W_{0} (\frac{16}{3}) < x < W_{0} (\frac{16}{3})

Interval Notation

(- W_{0} (\frac{16}{3}), W_{0} (\frac{16}{3}))

Decimal Notation

- 1.36374 \dots < x < 1.36374 \dots

Solution steps

3 ∣ x ∣ e^{∣ x ∣} < 16

Rewrite

3 ∣ x ∣ e^{∣ x ∣} < 16

in Lambert form:

e^{∣ x ∣} ∣ x ∣ < \frac{16}{3}

Solve

e^{∣ x ∣} ∣ x ∣ < \frac{16}{3} : ∣ x ∣ < W_{0} (\frac{16}{3})

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- W_{0} (\frac{16}{3}) < x < W_{0} (\frac{16}{3})

7 x^{2} + 12 x - 15 - 12 x = 2 x^{2}

(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8

∣ 2 x + 1 ∣ < 17

4 x - 9 \geq - 21

X (2 X - 5) = 3 (X - 2)

What is 3|x|e^{|x|}<16 ?
The solution to 3|x|e^{|x|}<16 is -\W_{0}(16/3)<x<\W_{0}(16/3)