Question

solve the equation and check the solution. if applicable, tell whether the equation is an identity or a contradiction.\\(-3x + 6x - 9 = 3(x - 5) - 4\\)\\(\\)\\(\\)select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\(\\)\\(\bigcirc\\) a. the solution set is \\(\\{\square\\}\\).\\(\\)\\(\\) (type an integer or a simplified fraction.)\\(\\)\\(\bigcirc\\) b. the solution set is \\{all real numbers\\}, so the equation is an identity.\\(\\)\\(\bigcirc\\) c. the solution set is \\(\varnothing\\), so the equation is a contradiction.

Explanation:

Step1: Simplify left side

Combine like terms: \(-3x + 6x - 9 = 3x - 9\)

Step2: Simplify right side

Distribute and combine: \(3(x - 5) - 4 = 3x - 15 - 4 = 3x - 19\)

Step3: Set equal and solve

\(3x - 9 = 3x - 19\)
Subtract \(3x\) from both sides: \(-9 = -19\) (False)

Answer:

C. The solution set is \(\varnothing\), so the equation is a contradiction.