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.