Question

Solve for x to determine if the equation has one, none, or infinite solutions.6(2x+4)−24=12x (1 point)ResponsesThe equation has no solution.The equation has no solution.The equation has one solution: x=−20.The equation has one solution: x equals negative 20 .The equation has infinite solutions.The equation has infinite solutions.The equation has one solution: x=0.

Answer 1

To solve the equation \(6(2x + 4) - 24 = 12x\), we will first simplify the left side.

1. Distribute \(6\) into the parentheses:
\[
6(2x) + 6(4) - 24 = 12x
\]
which simplifies to:
\[
12x + 24 - 24 = 12x
\]

2. Simplifying \(24 - 24\) gives us:
\[
12x = 12x
\]

3. This equation, \(12x = 12x\), is always true for any value of \(x\).

Since both sides are the same regardless of the value of \(x\), this means that the equation has infinite solutions.

So the correct response is:
**The equation has infinite solutions.**