|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
–3 < y < 5
To solve the absolute value inequality |y + 4| < 1, we can break it down into two cases: when y + 4 is positive and when y + 4 is negative.
Case 1: When y + 4 is positive, the inequality becomes y + 4 < 1. Solving for y, we subtract 4 from both sides to get y < -3.
Case 2: When y + 4 is negative, the inequality becomes -(y + 4) < 1. Simplifying, we get -y - 4 < 1. Then, we add y to both sides and subtract 1 from both sides, giving us -y < 5. To get y alone, we multiply both sides by -1 and reverse the inequality sign, resulting in y > -5.
Therefore, the solutions to the inequality are -5 < y < -3.
To solve the inequality |y + 4| < 1, we need to consider two cases: when y + 4 is positive, and when y + 4 is negative.
Case 1: y + 4 is positive
If y + 4 is positive, the inequality becomes y + 4 < 1. Subtracting 4 from both sides gives y < -3.
Case 2: y + 4 is negative
If y + 4 is negative, the inequality becomes -(y + 4) < 1. Distributing the negative sign gives -y - 4 < 1. Adding 4 to both sides gives -y < 5. Multiplying both sides by -1 (and flipping the inequality sign) gives y > -5.
Combining the results from both cases, we have -5 < y < -3.