subtract x from both sides:

3x + 1 = x - 6

subtract 2x from both sides:
4x - 3 = 2x + 1

I will be happy to check your work. Get real.

really? You can't figure out what do do when it says

subtract x from both sides:
3x + 1 = x - 6
?????
3x+1-x = x-6-x
2x+1 = -6
2x = -7
x = -7/2

To solve these equations by subtracting a certain value from both sides, follow these steps:

1. Start with the given equation: 3x + 1 = x - 6

2. To isolate the variable term, we need to remove the x term on one side of the equation. To do this, subtract x from both sides:
(3x + 1) - x = (x - 6) - x
Simplifying, we get: 2x + 1 = -6

3. Now, let's solve the second equation: 4x - 3 = 2x + 1

4. Similarly, we want to isolate the variable term, so let's subtract 2x from both sides:
(4x - 3) - 2x = (2x + 1) - 2x
Simplifying, we get: 2x - 3 = 1

By subtracting x or 2x from both sides of an equation, we are essentially canceling out the x term on one side to make it easier to solve for the variable (x).