Question

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

Answer 1

To determine whether the equation has one solution, no solutions, or infinite solutions, let's first simplify the equation step by step.

The equation we have is:

\[
4x = 3(x + 5) - 15
\]

First, distribute the \(3\) on the right side:

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

This simplifies to:

\[
4x = 3x
\]

Next, we can isolate \(x\) by subtracting \(3x\) from both sides:

\[
4x - 3x = 0
\]

This simplifies to:

\[
x = 0
\]

Now, let's summarize our findings:

1. We simplified and found one specific solution: \(x = 0\).
2. We can check if this was the only solution by seeing if the original equation was consistent.

Substituting \(x = 0\) back into the original equation:

- Left side: \(4(0) = 0\)
- Right side: \(3(0 + 5) - 15 = 15 - 15 = 0\)

Both sides equal zero, verifying \(x = 0\) is indeed a solution.

Since we found a specific solution and there were no contradictions during the process of solving, **the equation has one solution: \(x = 0\)**.