|y+4|<1
A. -5<y<-3
B. -3<y<5
C. -4<y<1
D. 1<y<4
To solve the inequality |y+4|<1, we need to consider two cases: when y+4 is positive and when y+4 is negative.
First, assume y+4 is positive. In this case, |y+4| is simply y+4. So, the inequality becomes y+4<1.
Subtracting 4 from both sides, we get y< -3.
Second, assume y+4 is negative. In this case, |y+4| is -(y+4), which is -y - 4. So, the inequality becomes -y - 4 < 1.
Adding y to both sides, we get -4 < y + 1.
Subtracting 1 from both sides, we get -5 < y.
Combining the two cases, we find that -5 < y < -3 or -5 < y.
So, the correct answer is A. -5 < y < -3.
To solve the inequality |y+4| < 1, we need to consider two cases: one where y+4 is positive and another where y+4 is negative.
Case 1: y+4 is positive (y+4 > 0)
In this case, the inequality becomes y+4 < 1. To solve for y, we can simply subtract 4 from both sides of the inequality:
y + 4 - 4 < 1 - 4
y < -3
Case 2: y+4 is negative (y+4 < 0)
In this case, we need to solve for the opposite of the inequality. Multiplying both sides by -1, we get:
-(y+4) < 1. Simplifying further,
-y - 4 < 1. Adding 4 to both sides,
-y < 5. Finally, multiplying both sides by -1 and flipping the inequality:
y > -5
Therefore, the solution to the inequality |y+4| < 1 is -5 < y < -3.
Out of the given options, option A (-5 < y < -3) matches the solution to the inequality.