|y + 4| < 1
(1 point)
Responses
−5 < y < –3
−5 < y < –3
–3 < y < 5
–3 < y < 5
–4 < y < 1
–4 < y < 1
1 < y < 4
1 < y < 4
–3 < y < -5
To solve the inequality |y + 4| < 1, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: y + 4 is positive
When y + 4 is positive, the inequality becomes y + 4 < 1.
Solving this inequality, we subtract 4 from both sides:
y < 1 - 4
y < -3
Case 2: y + 4 is negative
When y + 4 is negative, the inequality becomes -(y + 4) < 1.
To solve this, we multiply both sides by -1, which reverses the inequality:
y + 4 > -1
Next, we subtract 4 from both sides:
y > -1 - 4
y > -5
Combining the two cases, we find that the solution is:
-5 < y < -3