|y+4| < 1
-5 < y < -3
-3 < y < 5
-4 < y < 1
1 < y < 4
The correct range for y is -4 < y < 1.
To solve the inequality |y+4| < 1, we need to consider two cases:
Case 1: When y+4 is positive, the inequality becomes y+4 < 1.
Solving this inequality step-by-step:
1. Subtract 4 from both sides: y < 1 - 4
2. Simplify: y < -3
Case 2: When y+4 is negative, the inequality becomes -(y+4) < 1.
Solving this inequality step-by-step:
1. Multiply both sides by -1 (which reverses the inequality): y+4 > -1
2. Subtract 4 from both sides: y > -1 - 4
3. Simplify: y > -5
Combining the solutions for both cases, we get: -5 < y < -3
So, the final solution for the inequality |y+4| < 1 is: -5 < y < -3.
To solve the inequality |y + 4| < 1, we can break it down into two separate cases:
Case 1: When y + 4 is positive or zero.
In this case, the absolute value of y + 4 simplifies to y + 4. So, the inequality becomes y + 4 < 1.
To solve this inequality, we subtract 4 from both sides:
y < 1 - 4
y < -3
Case 2: When y + 4 is negative.
In this case, the absolute value of y + 4 can be found by multiplying it by -1. So, the inequality becomes -1(y + 4) < 1.
To solve this inequality, we distribute -1 to both terms inside the parentheses:
-y - 4 < 1
Next, we add 4 to both sides:
-y < 1 + 4
-y < 5
To isolate y, we multiply both sides by -1. Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality symbol:
y > -5
Combining the solutions from both cases, we find that the solution to the inequality |y + 4| < 1 is:
-5 < y < -3
Therefore, the correct answer is -5 < y < -3.