Let's solve the equation step by step:
Given: \[ 14(8m + 12) - 7 = -2 \]
First, add 7 to both sides of the equation:
\[ 14(8m + 12) = -2 + 7 \] \[ 14(8m + 12) = 5 \]
Next, divide both sides by 14:
\[ 8m + 12 = \frac{5}{14} \]
Now, subtract 12 from both sides:
\[ 8m = \frac{5}{14} - 12 \]
To combine the terms on the right side, we need a common denominator. We can express 12 as a fraction:
\[ 12 = \frac{168}{14} \]
Now, substituting this into the equation:
\[ 8m = \frac{5}{14} - \frac{168}{14} \] \[ 8m = \frac{5 - 168}{14} \] \[ 8m = \frac{-163}{14} \]
Next, divide both sides by 8:
\[ m = \frac{-163}{14 \times 8} \] \[ m = \frac{-163}{112} \]
This result does not match any of the options given (m=−3, m=11, m=1, m = −78). Let's check the calculations again for clarity to ensure no errors were made.
The left side calculated through each individual step:
- \(14 * 8m + 14 * 12 - 7\)
- Which leads to error checks, leading at the boundary of negative values.
It seems it is an error check against available options.
None of the options presented match. Re-evaluation may suggest an issue with bounding options. Would help to provide feedback for any further inquiries.