Let's solve the given equation step-by-step to determine which option is equivalent to it.
The given equation is:
[tex]\[ 7m + 11 = -4(2m + 3) \][/tex]
First, let's distribute the [tex]\(-4\)[/tex] on the right side:
[tex]\[ 7m + 11 = -4 \cdot 2m - 4 \cdot 3 \][/tex]
[tex]\[ 7m + 11 = -8m - 12 \][/tex]
Next, we'll combine like terms. To do this, let's get all the terms involving [tex]\(m\)[/tex] on one side and the constants on the other side. We'll add [tex]\(8m\)[/tex] to both sides:
[tex]\[ 7m + 8m + 11 = -12 \][/tex]
[tex]\[ 15m + 11 = -12 \][/tex]
Then, subtract 11 from both sides to isolate the term with [tex]\(m\)[/tex]:
[tex]\[ 15m = -12 - 11 \][/tex]
[tex]\[ 15m = -23 \][/tex]
We have now isolated [tex]\(m\)[/tex] in the equation:
[tex]\[ 15m = -23 \][/tex]
This is the simplification of the given equation:
[tex]\[ \boxed{15m = -23} \][/tex]
Thus, the correct option is:
[tex]\[ \text{C. } 15m = -23 \][/tex]
