Sure, let's solve the given equation step-by-step:
The given equation is:
[tex]\[ -36 / (x - 1) + 7 = -2 \][/tex]
### Step 1: Isolate the Fraction
First, let's isolate the fractional term by subtracting 7 from both sides of the equation:
[tex]\[ -36 / (x - 1) + 7 - 7 = -2 - 7 \][/tex]
Simplifying this, we get:
[tex]\[ -36 / (x - 1) = -9 \][/tex]
### Step 2: Eliminate the Fraction
Next, to eliminate the fraction, we multiply both sides of the equation by [tex]\((x - 1)\)[/tex]:
[tex]\[ -36 = -9 \cdot (x - 1) \][/tex]
### Step 3: Simplify
Now, divide both sides by -9 to isolate [tex]\((x - 1)\)[/tex]:
[tex]\[ 4 = x - 1 \][/tex]
### Step 4: Solve for [tex]\(x\)[/tex]
Finally, solve for [tex]\(x\)[/tex] by adding 1 to both sides:
[tex]\[ 4 + 1 = x \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the equation is:
[tex]\[ x = 5 \][/tex]
