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Solve the equation.

[tex]\[ -10x + 1 + 7x = 37 \][/tex]

A. [tex]\( x = -15 \)[/tex]
B. [tex]\( x = -12 \)[/tex]
C. [tex]\( x = 12 \)[/tex]
D. [tex]\( x = 15 \)[/tex]

Sagot :

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]