Question

how many solutions does this equation have?
\\(\frac{15(x - 3)}{5} = 3(2x - 3)\\)
no solution
one solution
infinitely many solutions
solve the equation.

Explanation:

Step1: Simplify left side

Simplify \(\frac{15(x - 3)}{5}\) to \(3(x - 3)\), so the equation becomes \(3(x - 3)=3(2x - 3)\).

Step2: Distribute both sides

Distribute: \(3x - 9 = 6x - 9\).

Step3: Subtract \(3x\) from both sides

\(3x - 9 - 3x = 6x - 9 - 3x\), which simplifies to \(-9 = 3x - 9\).

Step4: Add 9 to both sides

\(-9 + 9 = 3x - 9 + 9\), so \(0 = 3x\).

Step5: Solve for x

Divide both sides by 3: \(x = 0\).

Since we found a unique solution \(x = 0\), the equation has one solution.

Answer:

The equation \(\frac{15(x - 3)}{5}=3(2x - 3)\) has one solution, and the solution is \(x = 0\). For the number of solutions, the answer is "One solution" (the option: One solution).