solve 3x + x + 6 = 10x - 6x + 6. select the correct choice below and, if necessary, fill in the answer box…

solve 3x + x + 6 = 10x - 6x + 6. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = b. the equation has infinitely many solutions. c. the equation has no solution.

solve 3x + x + 6 = 10x - 6x + 6. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = b. the equation has infinitely many solutions. c. the equation has no solution.

Answer

Answer:

B. The equation has infinitely many solutions.

Explanation:

Step1: Combine like - terms on both sides

On the left - hand side, $3x + x+6=(3 + 1)x+6=4x + 6$. On the right - hand side, $10x-6x + 6=(10 - 6)x+6=4x + 6$.

Step2: Analyze the resulting equation

We get $4x + 6=4x + 6$. Subtracting $4x$ from both sides gives $4x-4x + 6=4x-4x + 6$, which simplifies to $6 = 6$. This is a true statement for all values of $x$. So the equation has infinitely many solutions.