What is the general solution for 2=3sin(|5x|)+1 ?

The general solution for 2=3sin(|5x|)+1 is No Solution for x\in\mathbb{R}

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2=3sin(|5x|)+1

2 = 3 sin (∣ 5 x ∣) + 1

No Solution for x \in R

Solution steps

2 = 3 sin (∣ 5 x ∣) + 1

Switch sides

3 sin (∣ 5 x ∣) + 1 = 2

Move

1

to the right side

3 sin (∣ 5 x ∣) = 1

Divide both sides by

3

sin (∣ 5 x ∣) = \frac{1}{3}

Apply trig inverse properties

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

Solve

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn :

No Solution

Solve

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn :

No Solution

x = No Solution, x = No Solution

Since the equation is undefined for:

No Solution

No Solution for x \in R

sin (θ) = - \frac{1}{3}

sin (θ) = - \frac{1}{4}

sin (θ) cos (θ) = \frac{1}{2}

cos (θ) = \frac{- 3}{2}

sin (x) cos (x) = sin (2 x)

What is the general solution for 2=3sin(|5x|)+1 ?
The general solution for 2=3sin(|5x|)+1 is No Solution for x\in\mathbb{R}