Let's solve the equation step-by-step.
The given equation is:
[tex]\[ -10x + 1 + 7x = 37 \][/tex]
### Step 1: Combine like terms
First, we need to combine the like terms on the left-hand side:
[tex]\[ -10x + 7x = -3x \][/tex]
So, the equation simplifies to:
[tex]\[ -3x + 1 = 37 \][/tex]
### Step 2: Isolate the x-term
Next, we want to isolate the term that includes [tex]\( x \)[/tex]. To do this, we'll subtract 1 from both sides of the equation:
[tex]\[ -3x + 1 - 1 = 37 - 1 \][/tex]
This simplifies to:
[tex]\[ -3x = 36 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, we need to solve for [tex]\( x \)[/tex] by dividing both sides of the equation by -3:
[tex]\[ x = \frac{36}{-3} \][/tex]
This simplifies to:
[tex]\[ x = -12 \][/tex]
### Conclusion
The solution to the given equation is:
[tex]\[ x = -12 \][/tex]
Therefore, the correct answer from the given options is:
[tex]\[ \boxed{-12} \][/tex]
