Question

Solve the equation. Show your steps.

32x + 3 =27x − 5

Answer 1

To solve the equation \( 32x + 3 = 27x - 5 \), follow these steps:

1. **Isolate the variable term on one side**:
Subtract \( 27x \) from both sides of the equation to move all terms involving \( x \) to one side.

\[
32x - 27x + 3 = 27x - 27x - 5
\]

This simplifies to:

\[
5x + 3 = -5
\]

2. **Isolate the constant term**:
Next, subtract \( 3 \) from both sides to move the constant to the other side.

\[
5x + 3 - 3 = -5 - 3
\]

This simplifies to:

\[
5x = -8
\]

3. **Solve for \( x \)**:
Finally, divide both sides by \( 5 \) to isolate \( x \).

\[
x = \frac{-8}{5}
\]

Thus, the solution to the equation is:

\[
\boxed{-\frac{8}{5}}
\]