Sure, let's solve the given equation step-by-step to find the value of [tex]\( m \)[/tex].
The equation we are given is:
[tex]\[
-\frac{11}{12} m = -\frac{1}{6}
\][/tex]
### Step 1: Eliminate the negative signs
Both sides of the equation have a negative sign, so we can multiply both sides by [tex]\(-1\)[/tex] to make the equation simpler:
[tex]\[
\frac{11}{12} m = \frac{1}{6}
\][/tex]
### Step 2: Isolate [tex]\( m \)[/tex]
We need to solve for [tex]\( m \)[/tex]. To do this, we can multiply both sides of the equation by the reciprocal of [tex]\(\frac{11}{12}\)[/tex], which is [tex]\(\frac{12}{11}\)[/tex]:
[tex]\[
m = \frac{1}{6} \times \frac{12}{11}
\][/tex]
### Step 3: Simplify the right-hand side
Next, we multiply the fractions:
[tex]\[
m = \frac{1 \times 12}{6 \times 11} = \frac{12}{66}
\][/tex]
### Step 4: Simplify the Fraction
Now we simplify the fraction [tex]\(\frac{12}{66}\)[/tex] by dividing both the numerator and denominator by their greatest common divisor, which is 6:
[tex]\[
m = \frac{12 \div 6}{66 \div 6} = \frac{2}{11}
\][/tex]
So the solution to the equation is:
[tex]\[
m = \frac{2}{11}
\][/tex]
Therefore, the correct answer from the given multiple-choice options is:
[tex]\[
m = \frac{2}{11}
\][/tex]
