Final answer:
The solution to the equation -2|7-9c|+7=-15 involves isolating the absolute value, resulting in two possible solutions: c = -4/9 and c = 2.
Step-by-step explanation:
To solve the equation -2|7-9c|+7=-15, first isolate the absolute value expression. Begin by subtracting 7 from both sides of the equation resulting in -2|7-9c| = -22.
Next, divide both sides of the equation by -2 to get the absolute value by itself: |7-9c| = 11.
Now, split the equation into two separate equations to account for the nature of the absolute value, which can be either positive or negative:
7-9c = 11 and 7-9c = -11.
Solving these two equations individually we get two possible solutions:
For 7-9c = 11, subtract 7 from both sides to get -9c = 4, and then divide by -9 to find c = -4/9.
For 7-9c = -11, subtract 7 from both sides to get -9c = -18, and then divide by -9 to find c = 2.
Thus, the solutions to the equation are c = -4/9 and c = 2.