Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex] from the given options.
The given equation is:
[tex]\[
-10x + 1 + 7x = 37
\][/tex]
### Step 1: Combine Like Terms
First, we need to simplify the left-hand side of the equation by combining like terms.
[tex]\[
-10x + 7x + 1 = 37
\][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[
-3x + 1 = 37
\][/tex]
### Step 2: Isolate the Variable Term
Next, we want to isolate the variable term [tex]\(-3x\)[/tex]. To do this, subtract 1 from both sides of the equation:
[tex]\[
-3x + 1 - 1 = 37 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
-3x = 36
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[
x = \frac{36}{-3}
\][/tex]
Simplifying this, we obtain:
[tex]\[
x = -12
\][/tex]
So, the solution to the equation is [tex]\(-12\)[/tex].
### Step 4: Verify with Given Options
We are given the options:
- [tex]\( x = -15 \)[/tex]
- [tex]\( x = -12 \)[/tex]
- [tex]\( x = 12 \)[/tex]
- [tex]\( x = 15 \)[/tex]
From our calculated result, the correct value of [tex]\( x \)[/tex] is [tex]\(-12\)[/tex].
Thus, the solution to the equation [tex]\(-10x + 1 + 7x = 37\)[/tex] is:
[tex]\[
\boxed{-12}
\][/tex]
