Solve for x to determine if the equation has one, none, or infinite solutions.

Question

4x=3(x+5)−15 (1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has one solution: x=0.
The equation has one solution: x equals 0 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−10.

Answer 1

To solve the equation $4x=3(x+5)-15$, we will start by simplifying the right side.

1. Expand the right side: $$3(x+5)=3x+15$$ So, $$3(x+5)-15=3x+15-15=3x$$

2. Now, we have the equation: $$4x=3x$$

3. Next, we will subtract $3x$ from both sides: $$4x-3x=0$$ This simplifies to: $$x=0$$

Now we check the conclusions:

• The equation $4x=3(x+5)-15$ simplifies to $4x=3x$, which leads us to $x=0$.
• This means there is one solution.

Thus, the answer is: The equation has one solution: x=0.