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

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 no solution.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), let's first simplify the right side of the equation.

1. Distribute \( 3 \) in \( 3(x + 5) \):
\[
3(x + 5) = 3x + 15
\]

2. The equation now looks like this:
\[
4x = 3x + 15 - 15
\]

3. Simplify the right side:
\[
4x = 3x + 0
\]
Which simplifies to:
\[
4x = 3x
\]

4. Subtract \( 3x \) from both sides:
\[
4x - 3x = 0
\]
This simplifies to:
\[
x = 0
\]

Now that we have solved for \( x \), let's analyze the original equation to see how many solutions it has:

Since we isolated \( x \) and found a specific value, we can conclude:
**The equation has one solution: \( x = 0 \)**.

So the correct response is:
**The equation has one solution: x equals 0.**