\( 3|3-4 x|=15 x \) What is the solution to the given equation

To solve the equation \( 3|3-4x|=15x \), first divide both sides by 3, which simplifies the equation to \( |3-4x|=5x \). This absolute value equation can be split into two separate cases: 1. **Case 1:** \( 3-4x = 5x \) leads to \( 3 = 9x \) or \( x = \frac{1}{3} \). 2. **Case 2:** \( 3-4x = -5x \) leads to \( 3 = -x \) or \( x = -3 \). Now, check both solutions in the original equation to ensure they are valid: - When \( x = \frac{1}{3} \): \( 3|3 - 4(\frac{1}{3})| = 3|3 - \frac{4}{3}| = 3|\frac{5}{3}| = 5 = 15(\frac{1}{3}) \) (valid) - When \( x = -3 \): \( 3|3 - 4(-3)| = 3|3 + 12| = 3 \times 15 = 45\) while \( 15(-3) = -45 \) (not valid). Thus, the only solution is \( x = \frac{1}{3} \). Happy solving!