Question

Solve the equation |f + 5| = 75 for f.

a. f=375 and -375
b. f= 15 and -15
c. f=-70 and 80
d. f= 70 and -80

Answer 1

To solve the equation |f + 5| = 75, consider the two possible cases of the absolute value and solve for f separately. The solutions are f = 70 and f = -80.

Step-by-step explanation:

To solve the equation |f + 5| = 75 for f, we consider two cases because the absolute value of a number can be either positive or negative.

1. For the case where the quantity inside the absolute value is positive: f + 5 = 75. We subtract 5 from both sides to find f, which gives us f = 70.
2. For the case where the quantity inside the absolute value is negative: f + 5 = -75. We again subtract 5 from both sides and get f = -80.

Therefore, the solutions to the equation are f = 70 and f = -80.