Sure, let's solve the equation [tex]\(\frac{x-6}{2} = -1\)[/tex] step by step.
1. Equation given:
[tex]\[
\frac{x-6}{2} = -1
\][/tex]
2. Eliminate the denominator by multiplying both sides of the equation by 2 to get rid of the fraction:
[tex]\[
2 \cdot \frac{x-6}{2} = 2 \cdot (-1)
\][/tex]
Simplifying this, we obtain:
[tex]\[
x - 6 = -2
\][/tex]
3. Solve for [tex]\(x\)[/tex] by isolating [tex]\(x\)[/tex]. To do this, add 6 to both sides of the equation:
[tex]\[
x - 6 + 6 = -2 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
x = 4
\][/tex]
4. Verify the solution by substituting [tex]\(x\)[/tex] back into the original equation:
[tex]\[
\frac{4 - 6}{2} = -1
\][/tex]
Simplifying the numerator:
[tex]\[
\frac{-2}{2} = -1
\][/tex]
Which confirms:
[tex]\[
-1 = -1
\][/tex]
The left-hand side equals the right-hand side, so our solution [tex]\(x = 4\)[/tex] is correct.
Therefore, the solution to the equation [tex]\(\frac{x-6}{2} = -1\)[/tex] is:
[tex]\[
\boxed{x = 4}
\][/tex]
