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.
solve |2c +8| = |10c|
Answer in simplest fraction form
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