Question

Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15 (1 point)

Answer 1

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

1. Start by distributing the 3 in the term \(3(x + 5)\):

\[
3(x + 5) = 3x + 15
\]

2. Replace the right side of the equation:

\[
4x = 3x + 15 - 15
\]

3. Simplify the right side:

\[
4x = 3x + 0
\]

This simplifies to:

\[
4x = 3x
\]

4. Now, subtract \(3x\) from both sides:

\[
4x - 3x = 0
\]

This gives:

\[
x = 0
\]

5. Since we found a specific value for \(x\), the equation has one solution.

Thus, the solution is \(x = 0\) and the equation has **one solution**.