Question

Solve for x to determine if the equation has one, none, or infinite solutions. 6(2x+4)−24=12x (1 point) Responses The equation has infinite solutions. The equation has infinite solutions. - no response given The equation has one solution: x=0 . The equation has one solution: x is equal to 0. - no response given The equation has one solution: x=−20 . The equation has one solution: x is equal to negative 20. - incorrect The equation has no solution.

Answer 1

Let's solve the equation step by step to determine how many solutions it has.

We start with the equation:

\[ 6(2x + 4) - 24 = 12x \]

1. Distribute \(6\) on the left side:

\[
12x + 24 - 24 = 12x
\]

2. Simplify the left side:

\[
12x = 12x
\]

Now we have:

\[
12x = 12x
\]

3. This indicates a tautology, meaning both sides are always equal for any value of \(x\).

Since the equation simplifies to a statement that is true for all \(x\), it means that:

The equation has infinite solutions.

So, the correct response is:

**The equation has infinite solutions.**