Question

The equation below has two solutions:

∣N+4∣=1
One solution to the equation is -3. What is the other solution of the equation?

a) N=−5
b) N=−3
c) N=3
d) N=5

Answer 1

The other solution to the absolute value equation |N + 4| = 1, given that one solution is -3, is N = -5.

Step-by-step explanation:

The absolute value equation |N + 4| = 1 means that the quantity inside the absolute value, N + 4, can be either 1 or -1 (since absolute value measures distance from zero and does not account for direction). Solving for each scenario:

• If N + 4 = 1, then N = 1 - 4, which gives N = -3.
• If N + 4 = -1, then N = -1 - 4, which gives N = -5.

Since one solution to the equation is -3, the other solution must be N = -5. Therefore, the correct answer to the question is (a) N = -5.