|y+4|<1 solve
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 > 0
If y + 4 > 0, then the absolute value of y + 4 is equal to y + 4 itself. Thus, the inequality becomes y + 4 < 1.
Solving this inequality, we subtract 4 from both sides:
y + 4 - 4 < 1 - 4
y < -3
Case 2: y + 4 < 0
If y + 4 < 0, then the absolute value of y + 4 is equal to -(y + 4). Thus, the inequality becomes -(y + 4) < 1.
Solving this inequality, we multiply both sides by -1, which changes the direction of the inequality:
y + 4 > -1
Next, subtract 4 from both sides:
y > -1 - 4
y > -5
Combining the results from both cases, we have y < -3 or y > -5 as the solution to the inequality |y + 4| < 1.