Question

Solve for \(x\): \(4x-3=3x-9\).

Answer 1

To solve the equation \(4x - 3 = 3x - 9\), we start by isolating the variable \(x\).

First, we can subtract \(3x\) from both sides:

\[
4x - 3x - 3 = -9
\]

This simplifies to:

\[
x - 3 = -9
\]

Next, we add \(3\) to both sides to isolate \(x\):

\[
x - 3 + 3 = -9 + 3
\]

This simplifies to:

\[
x = -6
\]

Thus, the solution is

\[
\boxed{-6}
\]

To verify our solution, we can substitute \(x = -6\) back into the original equation:

\[
4(-6) - 3 = 3(-6) - 9
\]

Calculating the left side:

\[
4(-6) - 3 = -24 - 3 = -27
\]

Now, calculating the right side:

\[
3(-6) - 9 = -18 - 9 = -27
\]

Since both sides are equal, our solution \(x = -6\) is confirmed to be correct:

\[
\boxed{-6}
\]