+1518 Find all c such that |c + 5| - 3c = 10 + 2|c - 4| - 6|c|. Enter all the solutions, separated by commas.
+1950 First, let's find every possible interval with this equation.
We have c<−5,−5≤c<0,0≤c<4,c≥4
Now, we solve the equation for each inequality.
Case 1 - c<−5
−c−5−3c=10−2c+8+6c−8c−23=0c=−238
This root is greater than -5, so it is invalid.
Case 2 - −5≤c<0
c+5−3c=10−2c+8+6c−6c−13=0c=−136
This works!
Case 3 - 0≤c<4
c+5−3c=10−2c+8−6c6c=13c=136
This works!
Case 4 - c>4
c+5−3c=10+2c−8−6c2c+3=0c=−32
This is invalid.
Now, we have c=−136,136
Thanks! :)
+1950 First, let's find every possible interval with this equation.
We have c<−5,−5≤c<0,0≤c<4,c≥4
Now, we solve the equation for each inequality.
Case 1 - c<−5
−c−5−3c=10−2c+8+6c−8c−23=0c=−238
This root is greater than -5, so it is invalid.
Case 2 - −5≤c<0
c+5−3c=10−2c+8+6c−6c−13=0c=−136
This works!
Case 3 - 0≤c<4
c+5−3c=10−2c+8−6c6c=13c=136
This works!
Case 4 - c>4
c+5−3c=10+2c−8−6c2c+3=0c=−32
This is invalid.
Now, we have c=−136,136
Thanks! :)
