+280 Find all c such that |c+5| - 3c = 10. Enter all the solutions, separated by commas.
+1234 To solve the equation |c+5| - 3c = 10, we need to consider two cases based on the absolute value:
1. c + 5 \geq 0 , which gives us |c+5| = c + 5 .
2. c + 5 < 0 , which gives us |c+5| = -(c + 5) = -c - 5 .
Let's solve each case separately:
Case 1: c + 5 \geq 0
In this case, we have the equation:
c + 5 - 3c = 10
5 - 2c = 10
-2c = 5
c = -5/2
Case 2: c + 5 < 0
In this case, we have the equation:
-(c + 5) - 3c = 10
-c - 5 - 3c = 10
-4c - 5 = 10
-4c = 15
c = -15/4
So, the solutions are c =-5/2 and c = -15/4.
