Question

Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point) Responses The equation has no solution. The equation has no solution. The equation has one solution: x=−10. The equation has one solution: x equals negative 10 . The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=0. The equation has one solution: x equals 0 .

Answer 1

Let's solve the equation step by step:

The original equation is:
\[ 4x = 3(x + 5) - 15 \]

1. First, simplify the right side:
\[ 4x = 3x + 15 - 15 \]
\[ 4x = 3x \]

2. Next, subtract \(3x\) from both sides:
\[ 4x - 3x = 0 \]
\[ x = 0 \]

Now we've determined that \(x = 0\) is a solution. Since we derived a single value for \(x\), the equation has one solution.

Thus, the correct response is:
**The equation has one solution: x = 0.**