Question

solve for c:
$a = 11 + 4b - 4c$
options:
$c = \frac{a + 4b + 11}{-4}$
$c = \frac{a + b - 11}{-4}$
$c = \frac{a - b + 11}{-4}$
$c = \frac{a - 4b - 11}{-4}$

Explanation:

Step1: Isolate the term with c

Start with the equation \( a = 11 + 4b - 4c \). Subtract \( 11 \) and \( 4b \) from both sides to get \( a - 11 - 4b = -4c \).

Step2: Solve for c

Divide both sides by \( -4 \). So, \( c=\frac{a - 4b - 11}{-4} \) (which can also be rewritten by multiplying numerator and denominator by -1 as \( c=\frac{-a + 4b + 11}{4} \), but the form we derived matches the last option).

Answer:

\( c=\frac{a - 4b - 11}{-4} \) (the last option among the choices, e.g., if the last option is \( c=\frac{a - 4b - 11}{-4} \), then that's the answer. Based on the given options, the correct one is the last option with \( c=\frac{a - 4b - 11}{-4} \))