## Explanation

### Step 1: Combine Like Terms

Start by simplifying the left side of the equation:

$-3x + 10x + 1 = x + 4$Combine like terms:

$( -3x + 10x ) + 1 = x + 4$This simplifies to:

$7x + 1 = x + 4$### Step 2: Move Variables to One Side

Next, we need to isolate the variable $x$. To do this, subtract $x$ from both sides of the equation:

$7x + 1 - x = x + 4 - x$This simplifies to:

$6x + 1 = 4$### Step 3: Isolate the Variable

Subtract 1 from both sides to move the constant term to the right side:

$6x + 1 - 1 = 4 - 1$This simplifies to:

$6x = 3$### Step 4: Solve for $x$

Finally, divide both sides by 6 to solve for $x$:

$\frac{6x}{6} = \frac{3}{6}$This results in:

$x = \frac{1}{2}$### Conclusion

**The solution to the equation is $x = \frac{1}{2}$.**