5 x + 1 = − 3 x − 7

To solve the equation \( 5x + 1 = -3x - 7 \), follow these steps:

1. First, let's get all the \( x \) terms on one side and the constant terms on the other side. Start by adding \( 3x \) to both sides:

   \[ 5x + 3x + 1 = -7 \]

   This simplifies to:

   \[ 8x + 1 = -7 \]

2. Next, subtract \( 1 \) from both sides:

   \[ 8x = -7 - 1 \]

   This simplifies to:

   \[ 8x = -8 \]

3. Now, divide both sides by \( 8 \):

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

   Thus,

   \[ x = -1 \]

The solution to the equation is \( x = -1 \).