Find all c such that |c+5| - 3c = 10. Enter all the solutions, separated by commas.

ABJelly Mar 30, 2024

#1**-2 **

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.

Akhain1 Mar 30, 2024