Final answer:
The equation 3|2x+5|=9x-6 can be solved by considering the two cases of the absolute value expression being either non-negative or negative and solving the resulting equations for x, followed by a verification of the solutions.
Step-by-step explanation:
The student has asked to solve the equation 3|2x+5|=9x-6. To solve this equation, we start by considering the two cases for the absolute value:
- Case 1: 2x+5 is non-negative, then 3(2x+5) = 9x-6. Solving this will give us one or more potential solutions.
- Case 2: 2x+5 is negative, then 3(-2x-5) = 9x-6. Solving this will give us another set of potential solutions.
Each case requires simplification and solving for x. After finding the possible values of x, substitute them back into the original equation to verify if they are indeed solutions, discarding any that don't satisfy the original equation.