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

 Mar 30, 2024
 #1
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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.

 Mar 30, 2024

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