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Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x (1 point)

The equation has one solution: x=3.

The equation has one solution: x=−3.

The equation has no solution.

The equation has infinite solutions.

1 answer

Let's solve the equation step-by-step:

The original equation is:

\[ 3(x + 2) - 6 = 3x \]

  1. Distribute the 3 on the left side:

\[ 3x + 6 - 6 = 3x \]

  1. Simplify the left side:

\[ 3x = 3x \]

This means that both sides of the equation are exactly the same.

Since the equation simplifies to \( 3x = 3x \), this is true for all values of \( x \). Therefore, there are infinite solutions.

So, the answer is:

The equation has infinite solutions.