Final answer:
The equation 18 = 6 |c+1| has two solutions, arising from the two possible values of the absolute value expression: c = 2 and c = -4.
Step-by-step explanation:
The equation in question is 18 = 6 |c+1|. To find the number of solutions, we first divide both sides of the equation by 6 to isolate the absolute value expression, giving us |c+1| = 3.
Since the absolute value of a number is the distance of that number from 0 on the number line, there are two possible solutions: one where (c+1) is 3 and one where (c+1) is -3.
1) If c+1 = 3, then c = 3 - 1, which results in c = 2.
2) If c+1 = -3, then c = -3 - 1, which results in c = -4.
Therefore, there are two solutions to the equation 18 = 6 |c+1|.