Question

Solve using the principles together.​ Don't forget to check.
5xminus9equals11xplus15

Answer 1

To solve the equation \( 5x - 9 = 11x + 15 \), we will isolate \( x \) by following these steps:

1. **Rearranging the equation**: Start by getting all terms involving \( x \) on one side and the constant terms on the other side.

\[
5x - 11x = 15 + 9
\]

This simplifies to:

\[
-6x = 24
\]

2. **Isolate \( x \)**: Divide both sides by -6 to solve for \( x \).

\[
x = \frac{24}{-6}
\]

This gives:

\[
x = -4
\]

3. **Check the solution**: Substitute \( x = -4 \) back into the original equation to verify.

Original equation:

\[
5(-4) - 9 = 11(-4) + 15
\]

Calculate each side:

Left side:

\[
5(-4) - 9 = -20 - 9 = -29
\]

Right side:

\[
11(-4) + 15 = -44 + 15 = -29
\]

Both sides are equal, confirming that our solution is correct.

Thus, the solution is \(\boxed{-4}\).