solve for c.\n4 = -6|c - 4| + 4\nwrite your answers as integers or as proper or improper fractions in…

Explanation:

Step1: Isolate the absolute - value term

Subtract (4) from both sides of the equation (4=-6|c - 4|+4). [ \begin{align*} 4-4&=-6|c - 4|+4 - 4\ 0&=-6|c - 4| \end{align*} ]

Step2: Solve for the absolute - value equation

Divide both sides by (-6). We get (|c - 4| = 0). By the definition of the absolute value (|x|=0) if and only if (x = 0). So, if (|c - 4|=0), then (c-4 = 0).

Step3: Solve for (c)

Add (4) to both sides of the equation (c-4 = 0). [c=4]

Answer:

(c = 4)