solve |2c +8| = |10c|

Answer in simplest fraction form

1 answer

We can solve this equation by considering two cases:

Case 1:
If 2c + 8 and 10c have the same sign, then the absolute value signs are not necessary. So we can rewrite the equation as:
2c + 8 = 10c

Subtracting 2c from both sides:
8 = 8c

Dividing both sides by 8:
c = 1

Case 2:
If 2c + 8 and 10c have opposite signs, then the absolute value signs are necessary. So we can rewrite the equation as:
2c + 8 = -10c

Adding 10c to both sides:
12c + 8 = 0

Subtracting 8 from both sides:
12c = -8

Dividing both sides by 12:
c = -8/12 = -2/3

Thus, the solutions to the equation |2c + 8| = |10c| in simplest fraction form are c = 1 and c = -2/3.