Question

|c- 24| = 7c :D :D :D

Answer 1

Start by making this absolute value equation into two equations; one positive and one negative equation. The two equations will be: c - 24 = 7c and c - 24 = -7c.

Start by solving the positive equation first: c - 24 = 7c. Add 24 to both sides and subtract 7c from both sides of the equation.

-6c = 24, now divide both sides by -6 to find your first c value.

c = -4

Solve the negative equation next: c - 24 = -7c. Add 24 to both sides and add 7c to both sides of the equation.

8c = 24, divide both sides by 8 to isolate c and find your second c value.

c = 3

Substitute to see if these values actually work with the given absolute value equation. Substitute -4 for c.

|c - 24| = 7c ==> |(-4) - 24| = 7(-4)

Solving this equation gives us 28 = -28, and this is a false statement so -4 cannot be part of the solutions. Now check 3 by substituting it for c.

|c - 24| = 7c ==> |(3) - 24| = 7(3)

Solving this equation we get 21 = 21, and this is a true statement so our only possible solution is c = 3.

Answer 2

$c\geq0\\\\\\ |c- 24| = 7c\\\\c-24=7c \vee c-24=-7c\\\\6c=-24 \vee -8c=-24\\\\c=-4 \vee c=3\\\\-4\not \geq0\\\\\boxed{c=3}$