Question
|y + 4| < 1 (1 point) Responses −5 < y < –3 , –3 < y < 5, –4 < y < 1, 1 < y < 4
Answers
GPT 3.5
To solve the inequality |y + 4| < 1, we can set up two separate inequalities:
1) y + 4 < 1 (since the absolute value of any number is always positive)
Subtracting 4 from both sides, we get:
y < -3
2) -(y + 4) < 1 (we use the negative sign outside the absolute value)
Distributing the negative sign, we get:
-y - 4 < 1
Adding 4 to both sides, we get:
-y < 5
Dividing both sides by -1 (and reversing the inequality sign since we are dividing by a negative number), we get:
y > -5
Combining the solutions from both inequalities, we have:
-5 < y < -3
1) y + 4 < 1 (since the absolute value of any number is always positive)
Subtracting 4 from both sides, we get:
y < -3
2) -(y + 4) < 1 (we use the negative sign outside the absolute value)
Distributing the negative sign, we get:
-y - 4 < 1
Adding 4 to both sides, we get:
-y < 5
Dividing both sides by -1 (and reversing the inequality sign since we are dividing by a negative number), we get:
y > -5
Combining the solutions from both inequalities, we have:
-5 < y < -3